Homology theory in the AST III. Comparison with homology theories of Čech and Vietoris
Commentationes Mathematicae Universitatis Carolinae (1993)
- Volume: 34, Issue: 1, page 11-22
- ISSN: 0010-2628
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topGuričan, Jaroslav. "Homology theory in the AST III. Comparison with homology theories of Čech and Vietoris." Commentationes Mathematicae Universitatis Carolinae 34.1 (1993): 11-22. <http://eudml.org/doc/247509>.
@article{Guričan1993,
abstract = {The isomorphism between our homology functor and these of Vietoris and Čech is proved. Introductory result on dimension is proved.},
author = {Guričan, Jaroslav},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {alternative set theory; set-definable; homology theory; simplex; complex; Sd-IS of groups; alternative set theory; set-definable; homology theory; simplex; complex; Sd-IS of groups},
language = {eng},
number = {1},
pages = {11-22},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Homology theory in the AST III. Comparison with homology theories of Čech and Vietoris},
url = {http://eudml.org/doc/247509},
volume = {34},
year = {1993},
}
TY - JOUR
AU - Guričan, Jaroslav
TI - Homology theory in the AST III. Comparison with homology theories of Čech and Vietoris
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1993
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 34
IS - 1
SP - 11
EP - 22
AB - The isomorphism between our homology functor and these of Vietoris and Čech is proved. Introductory result on dimension is proved.
LA - eng
KW - alternative set theory; set-definable; homology theory; simplex; complex; Sd-IS of groups; alternative set theory; set-definable; homology theory; simplex; complex; Sd-IS of groups
UR - http://eudml.org/doc/247509
ER -
References
top- Alexandrov P.S., Combinatorial Topology (in Russian), Moskva (1947). (1947)
- McCord M.C., Non-standard analysis and homology, Fund. Math. 74 (1972), 21-28. (1972) Zbl0233.55005MR0300270
- Dowker C.H., Homology groups of relations, Ann. Math 56 (1952), 84-95. (1952) Zbl0046.40402MR0048030
- Eilenberg S., Steenrod N., Foundations of Algebraic Topology, Princeton Press (1952). (1952) Zbl0047.41402MR0050886
- Garavaglia S., Homology with equationally compact coefficients, Fund. Math. 100 (1978), 89-95. (1978) Zbl0377.55006MR0494066
- Guričan J., Homology theory in the alternative set theory I. Algebraic preliminaries., Comment. Math. Univ. Carolinae 32 (1991), 75-93. (1991) MR1118291
- Guričan J., Homology theory in the AST II. Basic concepts, Eilenberg-Steenrod's axioms, Comment. Math. Univ. Carolinae 33 (1992), 353-372. (1992) Zbl0761.55004MR1189667
- Hilton P.J., Wylie S., Homology Theory, Cambridge University Press Cambridge (1960). (1960) Zbl0091.36306MR0115161
- Sochor A., Vopěnka P., Endomorphic universes and their standard extensions, Comment. Math. Univ. Carolinae 20 (1979), 605-629. (1979) MR0555178
- Sgall J., Witzany J., Dimension of indiscernibility equivalences, Comment. Math. Univ. Carolinae 28 (1987), 537-547. (1987) Zbl0629.03034MR0912582
- Vopěnka P., Mathematics in the Alternative Set Theory, Teubner-Texte Leipzig (1979). (1979) MR0581368
- Vopěnka P., Introduction to Mathematics in the Alternative Set Theory (in Slovak), ALFA Bratislava (1989). (1989)
- Wattenberg F., Non-standard analysis and the Theory of shape, Fund. Math. 98 (1978), 41-60. (1978) MR0528354
- Živaljevič R.T., Infinitesimals, microsimplexes and elementary homology theory, AMM 7 (1986), 540-544. (1986) MR0856293
- Živaljevič R.T., On a cohomology theory based on hyperfinite sums of microsimplexes, Pacific J. Math. (1987), 1 201-208. (1987) MR0883385
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