| 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:
|
http://hdl.handle.net/10338.dmlcz/118551 |
| . |
| Related article:
|
http://dml.cz/handle/10338.dmlcz/116944 |
| Related article:
|
http://dml.cz/handle/10338.dmlcz/118504 |
| . |
| 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 |
| . |
