Project detail

Continuous and set-theoretical methods in topological and algebraic structures

Duration: 01.01.2000 — 31.12.2002

Funding resources

Czech Science Foundation - Standardní projekty

- whole funder (2000-01-01 - not assigned)

On the project

Řešitelé se pokusí vyřešit některé obtížné problémy z oblasti množinově teoretické topologie a teorie kategorií. Mezi jiným, soustředíme se na sekvenční topologii na Booleových algebrách, na maximální skoro disjunktní systémy na množině přirozených čísel, na terminální pojmy v jazyce teorie množin, na kompaktní podmnožiny v prostorech spojitých funkcí, na spojitost v kontextu algebraických struktur a na vlastnosti součinů. Hlavní aspekty, které se různými způsoby kombinují, jsou: kombinatorický a kategoriální přístup, souvislosti s Booleovými algebrami, funkcionální analýzou, teorií míry a teorií generických rozšíření modelů teorie množin.

Description in English
The researchers will try to solve several difficult problems from the field of set-theoretical topology and category theory. Among others, we concentrate on the sequential topology on Boolean algebras, on maximal almost disjoint families on the set of natural numbers, on the terminal notions in the language of set theory, on the compact subsets of the spaces of continuous functions, on the continuity on algebraic structures and on the properties of products. The main aspects, used and combined in various ways, are: The combinatorial and categorical approach, the connections with Boolean algebras, functional analysis, measure theory and theory of generic extensions of models of set theory.

Mark

GA201/00/1466

Default language

Czech

People responsible

Hušek Miroslav, prof. RNDr., Dr.Sc. - fellow researcher
Kovár Martin, doc. RNDr., Ph.D. - fellow researcher
Pelant Jan, RNDr., Dr.Sc. - principal person responsible

Units

Department of Mathematics
- co-beneficiary (2000-01-01 - 2002-12-31)
Institute of Mathematics of the CAS, v. v. i.
- beneficiary (2000-01-01 - 2002-12-31)

Results

KOVÁR, M. On the weak reflections in some classes of topological spaces. In Abstracts of the First Turkish International Conference on Topology and Its Applications. Istanbul University, 2000. p. 17 ( p.)
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ŠLAPAL, J. A digital analogue of the Jordan curve theorem. Discrete Applied Mathematics, 2004, vol. 139, no. 1, p. 231 ( p.)ISSN: 0166-218X.
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KOVÁR, M. Problem 540 is (almost) solved. In Abstracts of the Ninth Prague Topological Symposium. Matematicko-fyzikální fakulta Univerzity Karlovy, 2001. p. 45 ( p.)
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KOVÁR, M. On dualizations of topological systems. In Abstracts of the Second Workshop on Formal Topology. Venezia (Venice, Benátky), Itálie: University of Padova and University of Venezia, 2002. p. 4 ( p.)
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KOVÁR, M. On iterated dualizations of topological spaces and structures. In Abstracts of the Workshop on Topology in Computer Science. New York, Spojené státy americké: City College, City University of New York, 2002. p. 11 ( p.)
Detail

KOVÁR, M. On iterated dualizations of topological structures. In Abstract of the International Conference on Topology and Its Applications - Topology in Matsue. Matsue, Japonsko: Shimane University in Matsue Osaka university, 2002. p. 42 ( p.)
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KOVÁR, M. Sequence of dualizations of topological spaces is finite. In Proceedings of the Ninth Prague Topological Symposium. 2002. p. 181 ( p.)ISBN: 0-9730867-0-X.
Detail

ŠLAPAL, J. A Jordan Curve Theorem with Respect to Certain Closure Operations on the Digital Plane. ELECTRONIC NOTES IN THEORETICAL COMPUTER SCIENCE, 2001, vol. 46, no. 1, p. 1 ( p.)ISSN: 1571-0661.
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ŠLAPAL, J. Convergence Structures for Categories. Applied Categorical Structures, 2001, vol. 9, no. 6, p. 557 ( p.)ISSN: 0927-2852.
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KOVÁR, M. On 3-topological version of $\theta$-regularity. International Journal of Mathematics and Mathematical Sciences, 2000, vol. 23, no. 6, p. 393 ( p.)ISSN: 0161-1712.
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KOVÁR, M. A Note on Ragahvan-Reilly's Pairwise Paracompactness. International Journal of Mathematics and Mathematical Sciences, 2000, vol. 24, no. 2, p. 139 ( p.)ISSN: 0161-1712.
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KOVÁR, M. A generalization of $\theta$-regularity and bitopological covering properties. Acta Mathematica Hungarica, 2000, vol. 88, no. 1, p. 95 ( p.)ISSN: 0236-5294.
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KOVÁR, M. A note on the comparison of topologies. International Journal of Mathematics and Mathematical Sciences, 2001, vol. 26, no. 4, p. 233 ( p.)ISSN: 0161-1712.
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KOVÁR, M. On weak reflections in some superclasses of compact spaces I. Topology Proceedings, 2002, vol. 25, no. 1, p. 575 ( p.)ISSN: 0146-4124.
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KOVÁR, M. A Solution of Problem 540. 2001, vol. 2001, no. 470, p. 1 ( p.)
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ŠLAPAL, J. Compactness with respect to a convergence structure. Quaestiones Mathematicae, 2002, vol. 25, no. 1, p. 19 ( p.)ISSN: 1607-3606.
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ŠLAPAL, J. Closure operations for digital topology. Theoretical Computer Science, 2003, vol. 305, no. 1-3, p. 457-471. ISSN: 0304-3975.
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KOVÁR, M. On weak reflections in some classes of topological spaces II. In IV Iberoamerican Conference o Topology. University of Coimbra, 2001. p. 32 ( p.)
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Responsibility: Pelant Jan, RNDr., Dr.Sc.