Věra Trnková

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Věra Trnková (born March 16, 1934 in Berehove , today Ukraine ; † May 27, 2018 ) was a Czech mathematician and university professor who was known for her work in topology and category theory.

Life and research

Trnková received her high school diploma in Prague and studied mathematics at Charles University from 1952 . She researched general topology with Miroslav Katětov and obtained a master’s degree in 1957 . In 1961 she did her doctorate as a doctoral student with Eduard Čech with the dissertation: Non-F-Topologies. In 1989 she received the Dr.Sc. Degree corresponding to a habilitation. In 1960 she became an assistant professor at Charles University, an associate professor in 1967, a senior researcher in 1986 and a full professor in 1991. In 1999 she retired. Despite starting her career in general topology, she switched to category theory as early as 1962. Her work in this area included the investigation of formal completions of categories, the embedding of categories in categories of topological spaces, the category-theoretical automaton theory and the isomorphism of product objects in categories. For example, she introduced the concept of almost complete nesting and proved that algebraic categories can always be nested almost completely in the category of compact topological spaces. This result has significantly changed the application of categories in other mathematical disciplines. The theory of set functors that she and her students developed has also influenced the work of many authors and has also become the basis for the application of categories in various areas of theoretical computer science . She was the author of over 160 research papers and two monographs. She was a member of the Editorial board of Algebra Universalis and the Editorial board of Scientiae Mathematicae Japonicae.

Publications (selection)

  • On convergence of sequences of functions, Comment. Math. Univ. Carolinae, 2: 1-12 (1961).
  • On category theory (in Russian), Comment. Math. Univ. Carolinae 3: 9-35 (1962).
  • Concerning the closure of classes of spaces by omega-maps (in Russian), DAN SSSR 156 (1962), 272-274.
  • Unions of strongly paracompact spaces (in Russian), DAN SSSR 146 (1962), 43-45.
  • Concerning the closure of classes of spaces by omega-maps (in Russian), Czechosl. Math. J. 14 (89), 1964, 327-340.
  • Topologies on products and decomposition of topological spaces, Czechosl. Math. J. 14 (89), 1964, 527-547.
  • Sum of categories with amalgamated subcategory, Comment. Math. Univ. Carolinae 6: 449-474 (1965).
  • Limits in categories and limit preserving functors, Comment. Math. Univ. Carolinae 7: 1-73 (1966).
  • Universal categories, Comment. Math. Univ. Carolinae 7: 143-206 (1966).
  • Universal category with limits of finite diagrams, Comment. Math. Univ. Carolinae 7: 447-456 (1966).
  • Completions of small subcategories, Comment. Math. Univ. Carolinae, 8: 581-633 (1967).
  • Strong embedding of category of all grupoids into category of semigroups, Comment. Math. Univ. Carolinae, 9: 251-256 (1968).
  • Some properties of set functors, Comment. Math. Univ. Carolinae 10: 323-352 (1969).
  • Nonconstant continuous maps of spaces and of their $ \ beta $ -compactifications, Topology and its Applications 33 (1989), 47-62.
  • Simultaneous representations by products in categories, in: Categorical Topology and its Relation to Analysis, Algebra and Combinatorics, edited by J. Adámek and S. Mac Lane, World Scientific, 1989, 410-431.
  • Products of metric, uniform and topological spaces, Comment. Math. Univ. Carolinae 31: 167-180 (1990).
  • Automorphisms of orthomodular lattices and symmetries of quantum logics, Foundations of Physics 21 (1991), 855-860.
  • Functorial selection of morphisms, in: Category Theory '91, Canadian Math. Society, Conference Proceedings 13 (1992), 435-447.
  • Rigid points and rigidity creating properties, in: Recent Developments of General Topology and its Applications, International Conference in Memory of Felix Hausdorff (1868-1942), Mathematical Research 67, Berlin 1992, 303-308.
  • Universal concrete categories and functors, Cahier's Topo. Geom. Diff. Cat. 1993, 34: 239-256.
  • Semirigid spaces, Trans. Amer. Math. Soc. 1994, 343: 305-325.
  • Universities, Appl. Cat. Structures 2: 173-185 (1994).
  • Continuous and uniformly continuous maps of powers of metric spaces, Topology and its Application 63 (1995), 189-200.
  • Clone segments in Top and Unif, in: Eraldo Giuli (ed.): Categorical Topology, 249-268, 1996 Kluwer Academic Publishers.
  • Simultaneous problems of clone segments in Top and in Unif, in: Eraldo Giuli (ed.): Categorical Topology, 269-278, 1996 Kluwer Academic Publishers.
  • Algebraic theories, clones and their segments, Applied Categorical Structures 4 (1996), 241-249.
  • Co-connected spaces, Serdica Math. J. 24 (1998): 25-36.
  • Representability and local representability of algebraic theories, Alg. Universalis 39 (1998), 121-144.
  • Representation of algebraic theories and non-expanding maps, J. Pure Appl. Alg. 146 (2000), 45-75.
  • Spaces without nonconstant maps into Y, Applied Categorical Structures 8 (2000), 407-424.
  • Maps of finite powers of metric spaces (recursive conditions for spaces at work), Topology and its applications 108 (2000), 277-301.
  • with Aleš Pultr: Combinatorial, algebraic and topological representations of groups, semigroups and categories, North Holland Mathematical Library 22, North Holland, 1980
  • with Jiří Adámek : Automata and Algebras in Categories in Mathematics and Their Applications 37, Kluwer, 1990

literature

  • Adámek, Jiří; Katětov, Miroslav: Věra Trnková's unbelievable 60. (English). Mathematica Bohemica, vol. 119 (1994), issue 2, pp. 216-224.

Web links

personal data
SURNAME Trnková, Věra
ALTERNATIVE NAMES Trnková-Šedivá, Věra
BRIEF DESCRIPTION Czech mathematician and university professor
DATE OF BIRTH March 16, 1934
PLACE OF BIRTH Berehove , Ukraine
DATE OF DEATH May 27, 2018