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**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 Phone: (371) 703 3725 |

* Born*: December 5, 1948 Riga, Latvia

Interests:

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

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

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

Education

- 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

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Experience:

- 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 –

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Honours and Awards:

- 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

Professional Activities and Memberships:

- 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)

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Recent/Representative Publications:

- 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.
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*Fuzzy Sets and Systems*, 2005, vol.155, pp.150-163.

**Courses:**

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

Other universities and colleges:

- 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 - )

*Last update 26.02.2007*