ALEXANDER SOSTAK (SHOSTAK)

Professor, Dr.habil.math. ALEXANDER SOSTAK (SHOSTAK) Head of the Section of Mathematical Analysis, Department of Mathematics, Faculty of Physics and Mathematics, University of Latvia Head of the Laboratory of Algebra and Topology Institute of Mathematics, Latvian Academy of Sciences and University of Latvia. Zellu iela 8, Riga, LV-1002 Latvia Phone: (371) 703 3725 Fax (371) 703 3701 E-mail: sostaks@lanet.lv; sostaks@latnet.lv

 Born: December 5, 1948 Riga, Latvia

• General Topology

    (Cardinal invariants of topological spaces, extension of continuous mappings, theory of retracts and extensors, shapes,      generalised metric spaces, compactness type properties);

• Category Theory
• L-Valued Topological and Algebraic Structures
• Fuzzy Sets. Applications of Fuzzy Sets and Fuzzy Structures
• Many-Valued Logics

Languages: Latvian, Russian, English, German, and Croatian 

• University of Latvia (Faculty of Physics and Mathematics), 1971

• Dr.math. (Candidate of Sciences in the former USSR), Moscow Lumumba University, 1975
• Post-doc: University of Zagreb, Zagreb, former Yugoslavia, 1979
• Dr.habil.math. (Doctor of Science in the former USSR), University of Latvia, 1993
• Professor, University of Latvia, 1993

• Assistant Professor, Associated Professor, Professor, Faculty of Physics and Mathematics, University of Latvia, 1974 -
• Head of the Section of Mathematical Analysis, Faculty of Physics and Mathematics, University of Latvia, 1999 –
• Visiting Professor, Rhodes University, Grahams town, Republic of South Africa, 1993
• Head of the Laboratory of Algebra and Topology, Institute of Mathematics, Latvian Academy of Sciences and Latvian University, 1997 –

• Corresponding Member, Latvian Academy of Sciences, 2004
• Member of the European Academy of Science (Section of Mathematical Sciences with the citation  " For outstanding and lasting contributions to mathematical sciences, fundamental developments in mathematical analysis and leadership in education"), 2003

• Member of the Board, Latvian Mathematical Society (1993- ), President (1997 – 2001)
• Member of the Board, Soviet (later Russian) Association of Fuzzy Structures Systems (1988 - 1994)
• Member, American Mathematical Society, 1990 –
• Member, South Africa Mathematical Society, 1994 -

• Member of the Editorial Advisory Board of Journals: Fuzzy Systems and Structures, 2001 - ; Matematicki Vesnik (Beograd, Serbia), Iranian Journal of Fuzzy Systems
• Vice Editor in Chief of Acta University Latviensis, ser Math., 2002 -
• Referee of Zentralblatt Math., Mathematical Reviews, Referativnyj Zhurnal (Moscow, Russia).
• Member of the Steering Committee of the Annual North American Topological Conferences (1998 – 2001)

• A.Shostak. Two decades of fuzzy topology: Basic ideas, concepts and results. – Russian Math. Surveys, 1989, 44, N 6 (270), pp.99-147 (in Russian); English translation:1989, vol.44, N 6, pp. 125-186.
• A.Sostak. On decomposition of a space into certain subspaces and cl-cardinality of a topological space. Ju.Bregman, B.Shapirovski). – Topology and Appl., 1994, vol. 57, pp. 295-306.
• A.Sostak. Basic structures of fuzzy topology, Part I. – J. of Math. Sciences, 1996, vol. 78, pp. 662-701.
• A.Sostak. Axiomatic foundations of fixed-basis fuzzy topology. (Coauthors U.Hohle) – In: The Handbook of Fuzzy Sets Series, 1999, vol. 3: Mathematics of Fuzzy Sets: Logic, Topology and Measure Theory. (Serial Eds: D. Dubois, H. Prade), Kluwer Academic Publ., Chapter 3, pp.123 - 273.
• A.Sostak On some fuzzy categories related to category L-TOP of L-topological spaces. – In: Topological and Algebraic Structures in Fuzzy Sets. Trends in Logics, vol. 30 (Eds. S.E. Rodabaugh and E.P. Klement), Kluwer Academic Publ., 2003, Chapter 12, pp. 337-374.
• A.Sostak L-valued categories: generalities and examples related to algebra and topology. – In: Categorical Structures and Their Applications (Eds. G.Preuss and W.Gaeler), World Scientific Publ., 2004, Chapter 10 , pp. 291-311.
• S.Asmuss, A.Sostak. On central algorithms of approximation under fuzzy information. – Fuzzy Sets and Systems, 2005, vol.155, pp.150-163.  

• Mathematical Analysis
• Functional Analysis
• Topology
• Set theory
• Category theory
• L-sets and L-valued structures (Alternative title: Fuzzy Sets and Fuzzy Structures)

• Calculus,
• Statistics
• Probability Theory
• General Topology

Research projects:

• A.Sostaks (Head of Project) Analysis of Topological, Functional and Algebraic Structures on Lattices of Fuzzy Sets. Latvian Council of Science (1991-1993)
• A.Sostaks (Head of Project) Investigation of Topological and Algebraic Structures on L-Lattices and Approximation of L-valued Functions. Latvian Council of Science (1994 – 1996)
• A.Sostaks (Head of Project). Investigation of L-topological and L-algebraic Structures and Categories; Development of L-valued Approximation Schemes. Latvian Council of Science (1997-2000)
• A.Sostaks (Head of Project). Research of L-valued Categories of Topological, Functional and Algebraic Structures and L-valued Approximative Schemes. Latvian Council of Science (2001-2004)
• A.Sostaks (Head of Project). Many-valued Structures in Topology, Algebra and Analysis: Research of Some Theoretical and Applied Problems. Latvian Council of Science (2005 - )

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Last update 26.02.2007