| Title:
|
Homology theory in the AST II. Basic concepts, Eilenberg-Steenrod's axioms (English) |
| Author:
|
Guričan, Jaroslav |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
33 |
| Issue:
|
2 |
| Year:
|
1992 |
| Pages:
|
353-372 |
| . |
| Category:
|
math |
| . |
| Summary:
|
Homology functor in the spirit of the AST is defined, its basic properties are studied. Eilenberg-Steenrod axioms for this functor are formulated and established. (English) |
| Keyword:
|
alternative set theory |
| Keyword:
|
set-definable |
| Keyword:
|
homology theory |
| Keyword:
|
simplex |
| Keyword:
|
complex |
| Keyword:
|
Sd-IS of groups |
| MSC:
|
03E70 |
| MSC:
|
03H05 |
| MSC:
|
55N35 |
| idZBL:
|
Zbl 0761.55004 |
| idMR:
|
MR1189667 |
| . |
| Date available:
|
2009-01-08T17:56:27Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118504 |
| . |
| Related article:
|
http://dml.cz/handle/10338.dmlcz/116944 |
| Related article:
|
http://dml.cz/handle/10338.dmlcz/118551 |
| . |
| Reference:
|
[A] Alexandrov P.S.: Combinatorial Topology.Moskva (1947),(in Russian). |
| Reference:
|
[C] Cord M.C.: Non-standard analysis and homology.Fund. Math. 74 (1972), 21-28. MR 0300270 |
| 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:
|
[G-Z] Guričan J., Zlatoš P.: Archimedean and geodetical biequivalences.Comment. Math. Univ. Carolinae 26 (1985), 675-698. MR 0831804 |
| 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:
|
[V1] Vopěnka P.: Mathematics in the Alternative Set Theory.Teubner-Texte Leipzig (1979). MR 0581368 |
| Reference:
|
[V2] Vopěnka P.: 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 93 (1986), 540-544. MR 0856293 |
| Reference:
|
[Ž2] Živaljevič R.T.: On a cohomology theory based on hyperfinite sums of microsimplexes.Pacific J. Math. (1987), 128 201-208. MR 0883385 |
| . |
