Georgi Dobromirov Dimov

Georgi Dobromirov Dimov

Professor
DSc

Complex Analysis and Topology

Email: 
gdimov@fmi.uni-sofia.bg
Phone: 
+359 2 8161-545
Room: 
FMI-212

Education

  • 1972: Magister, Mathematics, Moscow State University "M. V. Lomonosov"
  • 1977: PhD, Faculty of Mathematics and Informatics, Sofia University "St. Kl. Ohridski"
  • 2013: Dr. Habil. (=DSc), Faculty of Mathematics and Informatics, Sofia University "St. Kl. Ohridski"

Scientific Interests

 

  • General Topology
    • extensions of topological spaces (54D35) (compactifications and their remainders (54D40), realcompact extensions (54D60), locally compact extensions (54D45), regular and completely regular extensions (54D35), A-compactifications (54D35), z-compactifications (54D35));
    • proximity spaces and their generalizations (54E05);
    • hyperspaces (54B20);
    • spaces of continuous functions (Eberlein compacta, etc.) (54C35);
    • metric spaces and their generalizations, metrizability (54E35);
    • pseudo-radial, radial and almost radial spaces (54D55);
    •  special maps between topological spaces (54C10);
  • Categorical Topology
    • general theory of dualities (54H10, 54B30, 18A40, 18D05);
    • frames и locales (54B30);
    • dualities and equivalences (18A40);
  • Applications of general topology in theoretical computer science;
  • Boolean algebras (06Exx, 06E25,06E75,28A60).

Projects

  1. Project no. MI-1510/2005-2008 "Applied  Logics and Topological Structures" with the Bulgarian Ministry of Education and Science.
  2. Project no. 26/2006 "Categorical Topology" with the University of Sofia.
  3. Project no. 101/2007 "Categorical Topology and Computer Topology" with the University of Sofia.
  4. Project no. 136/2008 "General Topology and Computer Topology" with the University of Sofia.
  5. Project no. 005/2009 "General Topology and Categorical Topology" with the University of Sofia.
  6. Project no. 173/2010 "Duality, Equivalence and Representation Theorems and their Applications in General Topology" with the University of Sofia.
  7. Project no. DID 02/32/2009 with the Bulgarian Ministry of Education and Science.
  8. Project no. 93/2011 "Duality Theorems and their Applications in General Topology" with the University of Sofia.
  9. Project no. 140/2014 "Functional spaces and dualities" with the University of Sofia.
  10. Project no. 07/2015 "Contact algebras and extensions of topological spaces" with the University of Sofia.
  11. Project no. 07/2015 "Precontact algebras, dualities and hyperspaces" with the University of Sofia.
  12. Project no. DN02/15/19.12.2016  "Space, time and modality: relational, algebrical and topological models" with the Bulgarian Ministry of Education and Science

Teaching

Calculus I

Calculus II

Topology

General Topology

Topology for informaticians

Categorical topology

Seminar on topology

Seminar on category theory

Publications

Refereed publications
  1. On some special compactifications of rim-compact spaces, Compt. Rend. Acad. bulgare Sci., 30 (4), 1977, 483-486; (in Russian).
  2. Compactifications with discrete remainder, Compt. Rend. Acad. bulgare Sci., 30 (6), 1977, 797-800; (in Russian).
  3. Compactifications with a remainder of a special type, Coll. Math. Soc. János Bolyai, 23, Topology, Budapest (Hungary), 1978, 367-370.
  4. (jointly with D.Doitchinov) Supertopological spaces and locally compact extensions of topological spaces, Mitteilungen der Mathematischen Gesellschaft der DDR, 4, 1980, 41-44.
  5. Completely regular extensions of the completely regular spaces, Math. and Educ. Math. 9 (1980), 49-54; (in Russian).
  6. On the family of remainders of a completely regular space in its Hausdorff compactifications, Math. and Educ. Math. 10 (1981), 132-136; (in Russian).
  7. On the Stone duality, General Topology and its Relations to Modern Analysis аnd Algebra V, Proc. Fifth Prague Topol. Symp. 1981, J. Novak (ed.), Heldermann Verlag, Berlin 1982, 145-146.
  8. (jointly with D. Doitchinov) Regular extensions of regular topological spaces, Serdica Math. J., 8, 1982, 280-295; (in Russian).
  9. On compactifications of rim-compact spaces with remainders of a special type, Plisca, 6, 1983, 3-18; (in Russian).
  10. (jointly with B. A. Pasynkov) On a theorem of E. Čech, Comp. Rend. Acad. bulgare Sci., 36 (3), 1983, 305-308; (in Russian).
  11. On ĸ-metrizable Hausdorff compactifications of ĸ-metrizable spaces and a new class of spaces, including all separable metrizable spaces, Compt. Rend. Acad. bulgare Sci., 36 (10), 1983, 1257-1260.
  12. An axiomatic characterization of the Stone duality, Serdica Math. J., 10, 1984, 165-173.
  13. On Oz-compactifications, Berichte der Mathematisch-Statistischen Sektion im Forschungszentrum - Graz, Ber. n.236, 1985, 1-7.
  14. On ĸ-metrizable Hausdorff compactifications of ĸ-metrizable spaces, Serdica Math. J., 12 (1), 1986, 106-126; (in Russian).
  15. Regular, completely regular and other kinds of extensions of topological spaces, Compt. Rend. Acad. bulgare Sci., 39 (4), 1986, 9-12.
  16. Spaces whose remainders in a Stone-Čech or Freudenthal extension have a special form, Serdica Math. J., 12 (2), 1986, 171-188; (in Russian).
  17. (jointly with B. A. Pasynkov) Some analogues of a theorem of E. Čech, in the book “General Topology - Mappings of the Topological Spaces”, Moscow State University, 1986, 35-44; (in Russian).
  18. (jointly with R. Isler and G. Tironi) On functions preserving almost radiality and their relations to radial and pseudo-radial spaces, Comm. Math. Univ. Carolinae 28(4), 1987, 751-781.
  19. On Eberlein spaces and related spaces, Comptes rendus Acad. Sci., Paris, 304, Sér.I, 9, 1987, 233-235.
  20. (jointly with G. Tironi) Some remarks on almost radiality in function spaces, Acta Universitatis Carolinae - Math. Phys., 28 (2), 1987, 49-58.
  21. Baire subspaces of c0(Г) have dense Gδ metrizable subsets, Rendiconti Circolo Matemat. Palermo, Ser. II, Suppl. no.18, 1988, 275-285.
  22. On Rosenthal Theorem, General Topology and its Relations to Modern Analysis and Algebra, Proceedings of the Sixth Prague Topological Symposium 1986, Heldermann Verlag, Berlin 1988, p.660.
  23. (jointly with W. Tholen) A characterization of representable dualities, Categorical Topology and its Relations to Analysis, Algebra and Combinatorics (Prague, 1988), J. Adámek and S. MacLane (editors), World Scientific Publishing, Teaneck, NJ, 1989, 336-357.
  24. (jointly with G. Tironi) A new approach to proximities and compactifications, Compt. Rend. Acad. bulgare Sci., 45 (7), 1992, 5-8.
  25. (jointly with G. Tironi) A new approach to proximities and compactifications - II, Compt. Rend. Acad. bulgare Sci., 45 (8), 1992, 13-15.
  26. (jointly with W. Tholen) Groups of Dualities, Transactions of the American Mathematical Society, 336 (2), 1993, 901-915.
  27. (jointly with St. Barov and St. Nedev) On a theorem of H.-J. Schmidt, Compt. Rend. Acad. bulgare Sci., 46 (3), 1993, 9-11.
  28. Some remarks on the commutability between hyperspaces and subspaces, and on Schmidt’s conjecture, Compt. Rend. Acad. bulgare Sci., 47 (4), 1994, 5-8.
  29. On the commutability between hyperspaces and subspaces, and on Schmidt’s conjecture, Rendiconti dell’Istituto di Matematica dell’Università di Trieste, 25, Fasc. I-II, 1993, 175-194.
  30. (jointly with G. Tironi) Compactifications, A-compactifications and Proximities, Annali di Matematica pura ed applicata, (IV), 169 (1995), 87-108.
  31. (jointly with G. Tironi) Compactifications and A-compactifications of frames. Proximal frames, Mathematical Proceedings of the Cambridge Philosophical Society, 119, (1996), 321-339.
  32. (jointly with St. Barov and St. Nedev) On a question of M. Paoli and E. Ripoli, Bollettino U.M.I., (7) 10-A (1996), 127-141.
  33. (jointly with D. Vakarelov) On Scott consequence systems, Fundamenta Informaticae 33 (1998), 43-70.
  34. Regular and other kinds of extensions of topological spaces, Serdica Math. J. 24 (1) (1998), 99-126.
  35. (jointly with G. Tironi) Hausdorff Compactifications and Zero-One Measures, Mathematical Proceedings of the Cambridge Philosophical Society, 131 (2001), 495-505.
  36. (jointly with G. Tironi) Hausdorff Compactifications and Zero-One Measures - II, Applied General Topology, 3(1) (2002), 1-11.
  37. (jointly with A. Caterino and M. C. Vipera) A-compactifications and A-weight of Alexandroff spaces, Bollettino U.M.I. (8), 5-B (2002), 839-858.
  38. (jointly with F. Obersnel and G. Tironi) On Tychonoff-type Hypertopologies, Proceedings of the Ninth Prague Topological Symposium, (Prague, 2001) Topology Atlas, Toronto, 2002, pp. 51-70.
  39. (jointly with D. Vakarelov, I. Duentsch and B. Bennett) A proximity approach to some region-based theories of space, Journal of Applied Non-Classical Logic, v. 12, no.3-4 (2002), 527-559.
  40. (jointly with D. Vakarelov) Construction of all locally compact Hausdorff extensions of Tychonoff spaces by means of non-symmetric proximities, Questions and Answers in General Topology, 22 (2004), 43-56.
  41. (jointly with M.-C. Pedicchio and G. Tironi) Frames and Grids, Applied Categorical Structures, 12 (2004), 181-196.
  42. (jointly with D. Vakarelov) Topological Representation of Precontact Algebras, Relation Methods in Computer Science, W. MacCaull, M. Winter, I. Duentsch (Eds.), Lecture Notes in Computer Science, 3929 (2006), 1-16,  Springer-Verlag Berlin Heidelberg.
  43. (jointly with D. Vakarelov) Contact Algebras and Region-based Theory of Space: A Proximity Approach -- I, Fundamenta
    Informaticae 74(2-3) (2006), 209-249.
  44. (jointly with D. Vakarelov) Contact Algebras and Region-based Theory of Space: A Proximity Approach -- II, Fundamenta
    Informaticae  74(2-3) (2006), 251-282.
  45. (jointly with E. Ivanova) On paracompact and locally compact paracompact extensions, Questions and Answers in General Topology,
    25(2) (2007), 115-123.
  46. (jointly with E. Ivanova) On some categories arising in the theory of locally compact extensions, Mathematica Pannonica 19/2 (2008), 219-239.
  47. A generalization of De Vries' Duality Theorem, Applied Categorical Structures 17 (2009), 501-516.
  48. Some generalizations of the Fedorchuk Duality Theorem -- I, Topology Appl.  156 (2009), 728-746.
  49. Open and other kinds of map extensions over zero-dimensional local compactifications, Topology Appl., 157 (2010), 2251-2260.
  50. A de Vries-type duality theorem for the category of locally compact spaces and continuous maps - I, Acta Math. Hungar.  129(4) (2010), 314-349..
  51. A de Vries-type duality theorem for the category of locally compact spaces and continuous maps - II, Acta Math. Hungar.  130(1) (2011), 50-77.
  52. Open and other kinds of map extensions over local compactifications, Questions and Answers in General Topology 29(1) (2011), 35-56.
  53. Some Generalizations of the Stone Duality Theorem, Publicationes Mathematicae Debrecen 80(3-4) (2012), 255-293.
  54. A Whiteheadian-type description of Euclidean spaces, spheres, tori and Tychonoff cubes, Rend. Istit. Mat. Univ. Trieste,. 44 (2012),  45-74.
  55. An internal topological characterization of the subspaces of Eberlein compacta and related compacta -- I, Topology Appl. 169 (2014), 71–86.
  56. (jointly with D. Vakarelov) On the investigations of Ivan Prodanov in the theory of abstract spectra, Annuaire de l'Universite de Sofia "St. Kl. Ohridski", Faculte de Mathematiques et Informatique, 102 (2015) 31-70.
  57. (jointly with E. Ivanova) Yet another duality theorem for locally compact spaces, Houston Journal of Mathematics 42(2) (2016), 675-700.
  58. An internal topological characterization of the subspaces of Eberlein compacta and related compacta -- II, Topology Appl. 202 (2016), 440-453.
  59. (jointly with D. Vakarelov)  Topological representation of precontact algebras and a connected version of the Stone Duality Theorem -- I, Topology Appl. 227 (2017), 64-101.
  60. (jointly with E. Ivanova-Dimova, D. Vakarelov) A Generalization of the Stone Duality Theorem,  Topology and its Applications 221 (2017),  237–261.
 Non-refereed publications in ArXiv
  1. (jointly with Franco Obersnel, Gino Tironi) On Tychonoff-type hypertopologies, math.GN/0204121, 1-20 (preliminary version of the paper 38).
  2. A Generalization of De Vries' Duality Theorem, arXiv:0709.4041, 1-18 (preliminary version of the paper 47).
  3. Some Generalizations of the Fedorchuk Duality Theorem -- I, arXiv:0709.4495, 1-28 (preliminary version of the paper 48).
  4. Some Generalizations of the Fedorchuk Duality Theorem -- II, arXiv:0710.0181, 1-20 (the results of this paper are published as parts of the papers 51 and 52).
  5. A De Vries-type Duality Theorem for Locally Compact Spaces -- I, arXiv:0903.2589v2, 1-37 (preliminary version of the paper 50).
  6. A De Vries-type Duality Theorem for Locally Compact Spaces -- II, arXiv:0903.2593v4, 1-37.
  7. A De Vries-type Duality Theorem for Locally Compact Spaces -- III, arXiv:0907.2025, 1-31.
  8. Open and other kinds of extensions over zero-dimensional local compactifications, arXiv:0909.0982v2, 1-16 (preliminary version of the paper 49).
  9. Open and other kinds of extensions over local compactifications, arXiv:0910.3254, 1-22 (preliminary version of the paper 52).
  10. (jointly with E. Ivanova)  A new duality theorem for locally compact spaces, arXiv:1011.0079, 1-18. (preliminary version of the paper 56)
  11. A Whiteheadian-type description of Euclidean spaces, spheres, tori and Tychonoff cubes, arXiv:1203.4279, 1-29 (preliminary version of the paper 54).
  12. An internal topological characterization of the subspaces of Eberlein compacts and related compacts -- I, arXiv:1207.6802, 1-21 (preliminary version of the paper 55).
  13. An internal topological characterization of the subspaces of Eberlein compacta and related compacta -- II, arXiv:1412.2834, 1-22 (preliminary version of the paper 58).
  14. (jointly with D. Vakarelov) On the investigations of Ivan Prodanov in the theory of abstract spectra, arXiv:1507.05486, 1-51 (preliminary version of the paper 57).
  15. (jointly with D. Vakarelov)  Topological representation of precontact algebras and a connected version of the Stone Duality Theorem -- I, arXiv:1508.02220v3, 1-44.
  16. (jointly with E. Ivanova-Dimova, D. Vakarelov) A Generalization of the Stone Duality Theorem, arXiv: 1603.00932, 1-29 (preliminary version of the paper 60).
Other Publications
  1. Professor Doitchin Doitchinov, Mathematical Education, 5 (1987), 46-47 (in Bulgarian).
  2. 80 years from the birth of Professor Doitchin Doitchinov, Mathematical Forum, VIII  (2006), 6, 190-192  (in Bulgarian).

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