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Title: Homology theory in the AST III. Comparison with homology theories of Čech and Vietoris (English)
Author: Guričan, Jaroslav
Language: English
Journal: Commentationes Mathematicae Universitatis Carolinae
ISSN: 0010-2628 (print)
ISSN: 1213-7243 (online)
Volume: 34
Issue: 1
Year: 1993
Pages: 11-22
Category: math
Summary: The isomorphism between our homology functor and these of Vietoris and Čech is proved. Introductory result on dimension is proved. (English)
Keyword: alternative set theory
Keyword: set-definable
Keyword: homology theory
Keyword: simplex
Keyword: complex
Keyword: Sd-IS of groups
MSC: 03E70
MSC: 20F99
MSC: 55N35
idZBL: Zbl 0798.55005
idMR: MR1240199
Date available: 2009-01-08T18:00:40Z
Last updated: 2012-04-30
Stable URL:
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Reference: [A] Alexandrov P.S.: Combinatorial Topology (in Russian).Moskva (1947).
Reference: [C] McCord M.C.: Non-standard analysis and homology.Fund. Math. 74 (1972), 21-28. Zbl 0233.55005, MR 0300270
Reference: [D] Dowker C.H.: Homology groups of relations.Ann. Math 56 (1952), 84-95. Zbl 0046.40402, MR 0048030
Reference: [E-S] Eilenberg S., Steenrod N.: Foundations of Algebraic Topology.Princeton Press (1952). Zbl 0047.41402, MR 0050886
Reference: [G] Garavaglia S.: Homology with equationally compact coefficients.Fund. Math. 100 (1978), 89-95. Zbl 0377.55006, MR 0494066
Reference: [G1] Guričan J.: Homology theory in the alternative set theory I. Algebraic preliminaries..Comment. Math. Univ. Carolinae 32 (1991), 75-93. MR 1118291
Reference: [G2] Guričan J.: Homology theory in the AST II. Basic concepts, Eilenberg-Steenrod's axioms.Comment. Math. Univ. Carolinae 33 (1992), 353-372. Zbl 0761.55004, MR 1189667
Reference: [H-W] Hilton P.J., Wylie S.: Homology Theory.Cambridge University Press Cambridge (1960). Zbl 0091.36306, MR 0115161
Reference: [S-V] Sochor A., Vopěnka P.: Endomorphic universes and their standard extensions.Comment. Math. Univ. Carolinae 20 (1979), 605-629. MR 0555178
Reference: [S-W] Sgall J., Witzany J.: Dimension of indiscernibility equivalences.Comment. Math. Univ. Carolinae 28 (1987), 537-547. Zbl 0629.03034, MR 0912582
Reference: [V1] Vopěnka P.: Mathematics in the Alternative Set Theory.Teubner-Texte Leipzig (1979). MR 0581368
Reference: [V2] Vopěnka P.: Introduction to Mathematics in the Alternative Set Theory (in Slovak).ALFA Bratislava (1989).
Reference: [W] Wattenberg F.: Non-standard analysis and the Theory of shape.Fund. Math. 98 (1978), 41-60. MR 0528354
Reference: [Ž1] Živaljevič R.T.: Infinitesimals, microsimplexes and elementary homology theory.AMM 7 (1986), 540-544. MR 0856293
Reference: [Ž2] Živaljevič R.T.: On a cohomology theory based on hyperfinite sums of microsimplexes.Pacific J. Math. (1987), 1 201-208. MR 0883385


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