Publications

Journal papers in mathematics

 

1.       An answer to Heckmann’s open problem and Us --admitting spaces, C. Shen, Q. He, X. Xi and D. Zhao, Rocky Mountain J. Math.  55(2025), 1: 241 -254.

 

2.       The set of maximal points of an ω-domain need not be a Gδ-set, G. Li, C. Shen, K. wang, X. Xi and D. Zhao, Math. Structure Comp. Sci. 35(2025), e5.

 

3.       The Answers to Two problems on maximal points spaces of domains, X. Xi, C. Shen and D. Zhao, Topol. and Appl.  367(2025), 109340

 

4.       Johnstone’s non-sober dcpo and extension, D. Zhao, International Journal of Topology, (2025), 1-11.

 

5.       Reflectivity of some categories in domain theory, C. Shen, X. Xi and D. Zhao, Rocky Mountain J. Math. 54 (2024),  4: 1149-1166.

 

6.       The reflective hulls of some subcategories in the category of all T0 spaces,

H. Hou, Q. Li, H. Miao and D. Zhao, Houston Journal of mathematics 49(2023), 2:381-395.

 

7.       Not every countable complete distributive lattice is sober, H. Miao, Q. Li, X. Xi and D. Zhao, Math. Structure Comp. Sci. 33(2023), 9:809-831.

 

8.       On a problem about strictly completely regular ordered spaces posed by Lawson, X. Xiao, C. Shen, L. Gao and D. Zhao, Topol. and  Appl.  330(2023) 108489.

 

9.       Topological structure of the set of fuzzy numbers with the supremum metric, D. Liu, Z. Yang  and D. Zhao, Fuzzy Sets and Systems 453(2023), 15:37-56.

 

10.   Quasiexact Posets and Moderate Meet-continuity, Z. He, Z. Yang and D. Zhao, Electronic Journal in Theoretical Informatics and Computer Science, Vol 2 (2023).

 

11.   One-Step Closure, Weak One-Step Closure and Meet Continuity, H. Miao, Q. Li and D. Zhao,  Electronic Journal in Theoretical  Informatics and Computer Science, Vol 2 (2023).

 

12.   Further Studies on Open Well-filtered Spaces, C. Shen, X. Xi and D. Zhao, Electronic Journal in Theoretical Informatics and Computer Science, Vol 2 (2023).

 

13.   The sheaf representation of residuated lattices, H. Zhang and D. Zhao, Electronic Journal in Theoretical Informatics and Computer Science, Vol 2 (2023).

 

14.    The non-reflectivity of open well-filtered spaces via b-topology, C. Shen, X. Xi and D. Zhao, Houston J. Math. 48(2022), 4: 843-854.

 

15.   Maximal point spaces of interval posets, Z. He, Z. Yang and D. Zhao, Top. and Appl. 322(2022), 1-16,108314.

 

16.   Quasicontinuous spaces,  J. Lu, B. Zhao, K. Wang and D. Zhao,  Comment. Math. Univ. Caroline  63 (2022), no. 4, 513–526.

 

17.   Hofmann-Mislove type definitions of non-Hausdorff spaces, C. Shen, X. Xi, X. Xu and

D. Zhao, Mathematical Structures in Computer Science  32(2022), 1: 111-124.

 

18.   Directed complete posets determined by Scott closed set lattices and related work,

D. Zhao, Questions and Answers in General Topology  40(2022), 91-106. PDF

 

19.   Maximal point spaces of posets with relative lower topology, C. Shen, X. Xi and D. Zhao,  Filomat  35(2021) 8:2645-2661

 

20.    First countability, ω-Rudin spaces and well-filtered determined spaces, X. Xu, C. Shen,  X. 

        Xi and D. Zhao,  Topol. and  Appl.  (2021) 107775.

 

21.   On two problems about sobriety of topological spaces,  H. Miao, Q. Li  and D. Zhao,  Topol. and  Appl . 295 (2021), 107667, 10 pp.

 

22.   A unified approach to some non-Hausdorff topological properties,  Q. Li,  Z. Yuan and D. Zhao,  Mathematical Structures in Computer Science 30(2021), 9:997-1010.

 

23.   A complete Heyting algebra whose Scott space is non-sober, X. Xu, X. Xi and D. Zhao. Fund. Math.  252 (2021), 315-323.  

 

24.   Open well-filtered space, C. Shen, X. Xi, X. Xu and D. Zhao, Logical Method in Computer Science , 16 (2020), 4: 1-18.  

 

25.   Some open problems on well-filtered spaces and sober spaces, X. Xu and D. Zhao, Topol. and  Appl. (2020), 107540.

 

26.   Sl2 topology on T0  spaces,   C. Shen, H. Andradi,  D. Zhao and F. Shi,  Houston  J. Math. 49(2020), 2: 491-505.

 

27.   Well-filter determined spaces, X. Xu, C. Shen, X. Xi and D. Zhao, Topol. and  Appl.  282(2020) , 107323, Pg. 1-34.

 

28.   Sober Scott space is not always co-sober, C. Shen, G. Wu, X. Xi and D. Zhao, Topol. and Appl.  282(2020)，107316.

 

29.  First countability, -well-filteredness and reflection, X. Xu, C. Shen,  X. Xi and D. Zhao,  Topol. and  Appl.  279(2020), 107255.

 

30.   On topological Rudin’s lemma, well-filtered spaces and sober spaces, X. Xu and D. Zhao, Topol. and Appl.  272(2020), 107080.

 

31.   Topologies generated by families of sets and strong poset models,  D. Zhao, X, Xi and Y. Chen,  Topol. Proc.  56(2020), 249-261.

 

32.   Existence of well-filterification of T0 topological spaces,  G. Wu, X. Xi, X. Xu and D. Zhao, Topol. and Appl.  270(2020), 107044.

 

33.  On well-filter reflectors of  T0  spaces, C. Shen,  X. Xi, X. Xu and D. Zhao,  Topol. and  Appl.   267(2019), 106869.

 

34.   Some Results on Poset Models Consisting of Compact Saturated Subsets,

Q. He, G. Li, X. Xi and  D. Zhao, Electronic Notes in Theoretical Computer Science  345(2019), 77-85.

 

35.   Cσ-unique Dcpos and Non-maximality of the Class of Dominated Dcpos Regarding Γ-faithfulness,  L. Xu and  D. Zhao, Electronic Notes in Theoretical Computer Science  345(2019), 249-260.

 

36.   An universal Approach to Z–frame Envelopes of Semilattices,  G. Li, D. Zhao and  W. Ho,   Electronic Notes in Theoretical Computer Science  345(2019), 87-97.

         

37.   Weak Domain Models of T1 spaces,  C. Shen,   G. Wu, D. Zhao,   Electronic Notes in Theoretical Computer Science  345(2019), 219-232.

 

38.   Lattice-equivalence of convex spaces, C. Shen, S. J. Yang, D. Zhao  and  F. Shi,   Algebra   Universalis  80 (2019), no. 3, Art. 26, 19 pp .

 

39.  Dcpo models of Choquet complete and Baire spaces,  Q. He, X. Xi and D. Zhao, Results in Mathematics 74 (2019), no. 3, Art. 87, 16 pp.

 

40.   A new dcpo whose Scott topology is well-filtered but not sober,  D. Zhao, X. Xi and Y. Chen, Topol.  and  Appl.  252(2019), 1:97-102.

 

41.   A New Convergence Inducing the SI-Topology,  H.  Andrad,  C. Shen,  W. K.  Ho and D.   

 Zhao,  Filomat  32(2018), 17: 6017–6029

 

42.   A new topology on the space of primitives of  Henstock-Kurzweil Integrable Functions,   D. K. Sari , P. Y. Lee  and D. Zhao , 

Southeast Asian Bulletin of Math.  42(2018), 5: 719 –  728.

 

43.   Uniqueness of directed complete posets based on Scott closed set lattices,  D. Zhao and  L. Xu, Logical Method in Computer

 Science 14(2:10)(2018), pp 1-12. (Link)

 

44.   Spaces that have a bounded complete dcpo model,  D. Zhao and X. Xi,  Rocky  

 Mountain J. Math. 48(2018), 1: 141-156.

 

45.    Rank commutators of families of matrices,  F. Dong,  W. Ho and D. Zhao,   

 Southeast Asian Bulletin of Math.  42(2018), 15 – 30.

 

46.    Directed complete poset models of T1  spaces,  D. Zhao and X. Xi,  Math. Proc.  

 Cambridge Phil. Soc. 164 (2018), 125 –134.

 

47.    Maximal point  spaces of dcpos satisfying the Lawson condition,  X. Xi  and  D.

 Zhao,  Topol.  and  Appl. 230(2017), 417 – 424.

 

48.    2-Absorbing delta-primary ideals in commutative rings,  B. Fahid and D. Zhao,

 Kyungpook Mathematical Journal,  57 (2017), 2: 193—198.

 

49.    Maximal classes of spaces and domains determined by topologies on function  

  spaces of domains, X. Xi, H. Liu, W. K. Ho and D. Zhao, Topol. and

  Appl.  222 (2017), 278–292.

 

50.    Well-filtered spaces and their dcpo models,  X. Xi  and  D. Zhao, Math Structures  

  in  Computer Science  27 (2017), 4: 507–515.

 

51.     A new cardinal function on topological spaces,  D. K. Sari  and D. Zhao,  Applied 

  General Topology 18 (2017), 1: 75 – 90. PDF

 

52.     Open set lattices of subspaces of spectrum spaces,  Y. T. Nai and D. Zhao, 

   Demonstratio Mathematica 48(2015), 4: 637 – 652.

 

53.    On ideals of rings  of fractions and polynomials, Y. T. Nai and D. Zhao,  Kodai  

  Math.  J.  38(2015), 2: 333 - 342.

 

54.     Closure spaces and completions of posets,  D. Zhao,  Semigroup Forum   

   90(2015),  2:  545-555.

 

55.     On topologies defined by irreducible sets,   D. Zhao  and  W. K. Ho,   J.  Logical

   and Algebraic Methods in Programming 84(2015),  1: 185 – 195.  PDF           

 

56.     Reflexive index of a family of sets,  D. Zhao,  Kyungpook  Math.  J.  54(2014),  

  263-269.

 

57.     Principal mappings between posets, Y. T. Nai and D. Zhao,  Inter.  J. Math. Math. 

  Sciences  Article ID 754019, 2014.

 

58.    On the largest outscribed equilateral triangle,  F. Dong, D. Zhao and W. K. Ho, 

  The Mathematical Gazette  97(2014), 79 - 84

 

59.     Some New Intrinsic Topologies on Complete  Lattices and the Cartesian  

   Closedness of the Category of  Strongly Continuous Lattices,  X. Wu,  

   Q.  Li & D. Zhao, Abstract and Applied Analysis  Vol. 2013,  Article ID 942628,

   1 - 8.

 

60.    A stone type  duality for orthoposets,  D. Zhao,  Kochi  J.  Math. 8(2013), 19 - 34.

 

61.    Partial dcpo’s and some applications,  D. Zhao,  Archiv.  Math. 48(2012), 4: 243-

  260.

 

62.     Maximal outboxes of quadrilaterals, D. Zhao, International Journal of Math.  

  Education in Science and Technology  42(2011), 4: 534 - 540.

 

63.     A partial order on the set of continuous endomappings, D. Zhao, Houston J.

  Math.  37(2011), 311 – 326.

 

64.    On reflexive closed set lattices,  Z. Yang  and D. Zhao,  Commentationes

  Mathematicae Universitatis Carolinae  51(2010), 143 – 154.

 

65.    Dcpo-completion of posets,   D. Zhao  and  T. Fan,  Theoretical Computer Science     411(2010), 2167 – 2173.

 

66.   Poset models of topological spaces, D. Zhao,  In: Proceeding of International Conference on Quantitative Logic and

Quantication of Software (Global - Link Publisher, 2009), pp. 229-238. PDF

 

67.    Lattices of Scott-closed sets,  W. K. Ho and D. Zhao,  Commentationes

  Mathematicae Universitatis Carolinae 50(2009), 297 – 314.

 

68.    Gauges of Baire Class One functions,   Z. Atok, W.  K. Tang and D. Zhao, Journal   

  of Mathematical Analysis and Applications 343(2008),  866 - 870.

 

69.    Functions whose composition with Baire class one functions are baire class one,  

         D. Zhao, Soochow Journal of Mathematics  33(2007), 4:543 – 551.  PDF

 

70.     Reflexive families of closed sets,  Z. Yang and D. Zhao, Fund. Math. 192(2006),  

  111 – 120.

 

71.     Lim-inf convergence in partially ordered sets,  B. Zhao and D. Zhao, J. Math.

   Anal.  Appl. 309(2005),  701 – 708.

 

72.     The Riemann integral using ordered open coverings,  D. Zhao and P. Y.  Lee,

   Rocky Mountain  Math. 35(2005), 6: 2129 – 2147.

 

73.     A new compactness type topological property,  D. Zhao, Quaestiones

   Mathematicae  28(2005), 1 – 11.

 

74.     Adjunctions defined by mappings, D. Zhao,  J.  Indonesian Mathematical Society    

   11(2005), 2:163 – 173.

 

75.     On reflexive subobject lattices and reflexive enodomorphism algebras, D. Zhao,   

   Commentationes Mathematicae Universitatis Carolinae  44(2003), 23 – 32.

 

76.    On the limits of a class of sequences,  D. Zhao, T. Y. Lee, C. S. Lee  and S. F. Yap, 

         International Journal of Math. Education in Science and Technology 33(2002),

         1:123-127.

 

77.     d -primary Ideals of Commutative Rings,  D. Zhao,  Kyungpook Mathematical  

   Journal 41(2001), 17 – 22.

 

78.     Z-Join Spectra of  Z-Supercompactly Generated Lattices,  M. Erne and D.  Zhao,

  Applied Categorical Structures  9(2001), 1: 41 – 63.

 

79.     An equivalent definition of functions of the first Baire class, P. Y. Lee, W. K. Tang  

  and D. Zhao, Proc.  Amer. Math.  Soci.  129(2000),  8: 2273 – 2275.

 

80.    Monadicity of  Inj_0 over  Top,  D. Zhao and  B. Zhao,  J. Math. Res. Exposition

  20(2000), 4: 475 – 482.          

 

81.    Moore-Smith limits and the Henstock integral, G. I.  June, P. Y.  Lee and D. Zhao,

                 Real Analysis Exchange  24(1998/1999), 1:447 – 455.

 

82.     The categories of m-semilattices,  D. Zhao and B. Zhao, Northeastern

   Mathematics Journal  14(1998),  4: 419 – 430.

 

83.     On projective z-frames, D. Zhao, Canadian Mathematical Bulletin  40(1997),

   1:39 – 46.

 

84.      Semicontinuous lattices,  D. Zhao, Algebra Universalis  37(1997),  458 – 476.

 

85.     Bases of completely distributive lattices,  D. Zhao,   J. Fuzzy Math. 5(1997),  1:

          103 – 109.  MR1441019 (98f:06008)

 

86.     Nuclei on z-frames,  D. Zhao,  Soochow Journal of Mathematics  29(1996),

  1:  59 – 74. PDF

 

87.    Upper and Lower Henstock Integrals, P. Y. Lee and D. Zhao, Real Analysis

              Exchange  22(1996/1997), 734-739. 

 

88.    On the theory of φ-continuous posets, D. Zhao,   J. Engineering Math.  9(1992),

  1:1-6.

 

89.    Some characteristics of continuous lattices and completely distributive lattices,

  D.  Zhao,  Chinese Quarterly J. of Math.  1(1990), 2:162-165.    PDF

90.    Bi-Scott topologies on lattices, D. Zhao, Chinese Ann. Math.( Ser. A ) 10(1989),

  2:187 – 193. PDF

 

91.    The structures of  order  involution,   J. Shaanxi Normal University(Natural  

  Science Edition)  17(1989), 2: 1 - 4.

 

92.    Pseudo-uniformly continuous order homomorphisms on Fuzz,   D. Zhao,  Adv.   

         Math. (Beijing), 16 (1987),  3: 305--308.   .

 

93.    The N-compactness in L-fuzzy  topological  spaces,  D. Zhao,  J. Math.  Anal. 

  Appl.  128(1987),  11: 64 – 79.

 

94.     A new type of fuzzy connectedness, D. Zhao and G. Wang, Fuzzy Math.  4(1984), 

  4:15 -22. 

 

95.     The Fuzzy Decision of purchase in library. Y. Zhang, D.  Zhao, Z. Yang, Fuzzy  

   Math. 4(1983), 89-102.

 

96.     The continuity of the limit function of nets of continuous functions,  D. Zhao,  

   J.  Shaanxi Normal University 21(1981) 65 – 68.

 

Journal  papers  in Education Mathematics

 

97.   Some strategies of posing mathematics problems, D. Zhao and C. S. Lee,

       Discovering Mathematics, 28(2006), 1: 9 -14.

 

98.   On some maximum area problem II, D. Zhao, S. F. Yap and C. S. Lee,  

  Mathematical Medley  30(2003), 1: 23 – 29.

 

99.   On some maximum area problem I, D. Zhao, S. F. Yap and C. S. Lee,  

  Mathematical Medley  29(2002),  2:78 – 85.

 

100.    Asking converse questions and looking for extensions to Gauss’s method for

  summing  arithmetic progressions,  E. G. Tay and D. Zhao,   Math. Educators     

  6(2002), 2: 65 – 76.

 

101.   Different approaches to the solution of a simple problem, T. Y. Lee, D. Zhao, S. F. Yap and C. S. Lee, Discovering Mathematics 23(2001), 1: 1 – 9.

 

102.    A note on an invariant sum problem in Geometry, D. Zhao, T. Y. Lee, S. F. Yap 

      and C. S. Lee, Mathematical Medley 28(2001), 1:  9 – 12.

 

 

Conference papers published in  proceedings

 

103.    Dcpo models of T1  spaces,  D. Zhao and X. Xi, Proceedings of  TACL 2013, pp. 220-223. 

 

104.    A generalization of Dilworth’s principal elements, D. Zhao and Y. T.  Nai, In: Quantitative Logic and Soft Computing, pp. 573-580, World Scientific, 2012.

 

105.      Some principles and  guidelines for designing mathematics disciplinary tasks for Singapore schools,  D. Zhao, W. K. Cheng, K. M. Teo  and P.   Y. Lee, Proceeding of  AAMT&MERGA,  Australia,  pp. 1107 -1115, 2011.

 

106.     D-completions of net-convergence structures.  W. K. Ho, D. Zhao and W. S. Wee,   In: Quantitative Logic and Soft Computing, vol. 2,

  pp. 93 –  110,   Springer, 2010.

 

107.      Developing disciplinary tasks to improve mathematics assessment and pedagogy: An exploratory study in Singapore schools. L. Fan,  D. Zhao, W. K. Cheang  and K. M. Kok,   Procedia - Social and Behavioral Sciences,  vol. 2(2),  pp. 2000 – 2005,   Elsevier,  2010.

 

108.      Filter convergence structure in posets.  Asian Mathematics Conference (AMC), W. S. Wee, W. K. Ho and D. Zhao, 2009.

 

109.      Scott closed set lattices and applications, Proceeding of the 5th Seams – GMU International Conference on Mathematics and Its Applications,  pp. 1 -16,  Yogyakarta – Indonesia,  2007.

 

110.      Problem posing in teaching University Mathematics, D. Zhao and P. Y. Lee, Proceeding of the MERA – ERA Joint Conference, pp. 940 – 944,  1999.

 

 

Books/Book Chapters/Lecture Notes

111.     Beyond School Mathematics, Ho, W.K, Toh, P.C., Teo, K.M, Zhao, D. and  

 Hang,   K.H.,  IN: Mathematics Education in Singapore, Springer,  May 2019.

 

112.     Scaffolding and Constructing New problems for Teaching Mathematical Proofs in  the A-levels, IN: LEARNING EXPERIENCES TO PROMOTE MATHEMATICS 

 LEARNING,  World Scientific, June 2014.

 

113.     LINEAR ALGEBRA – An Easy Introduction, 

 Teo Kok Ming & Zhao Dongsheng,  August 2013, Mc Graw Hill.

 

114.     Plane Geometry ---Theorems, examples, exercises,  

 Zhao Dongsheng & Yap Sook Fwe, January 2011.

 

115.    An introduction to general topology (PDF)

 

 

 

Thesis

     MSc:  

                 N-compactness in L-fuzzy topological spaces,

                 Shaanxi Normal University, 1984.

     PhD:  

                Generalization of Continuous Lattices and Frames,

                University of Cambridge, 1992.

              

     Poster Diploma of Teaching High Mathematics:  

 

                Promote Active Learning in Mathematics,

                Nanyang Technological University, 1998

Others

  

 

1.      Ratio  of  volume  to surface area,  D. Zhao D, W. K. Cheang  and P. Y.  Lee,   Maths  Buzz, 

 Vol. 12(1), pg. 2-2, 2011.

 

2.      Characterizations of  Baire Class One functions,   SciTopics,  Elsevier,   Dec 2010  [Invited author]  

 

3.      Lattices  of   Scott  Closed sets ,   SciTopics,  Elsevier,   Jul 2010  [Invited author]

 

4.      Learning Mathematics Through Exploration and Connection.  D. Zhao, K. C. Ang, G.  Cheang, R.  Phang  and  W. K. Tang,   The NIE Researcher, Vol.1(2),   pp. 9 - 10, 2001. 

 

5.      Scott topology and sober spaces.  In:  Collection  of   Post  Graduate Students’  Research  Work,         

              Shaanxi  Normal  University,  Vol. 1,  pp. 189 – 194, 1984.