| Title:
|
Homology theory in the alternative set theory I. Algebraic preliminaries (English) |
| Author:
|
Guričan, Jaroslav |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
32 |
| Issue:
|
1 |
| Year:
|
1991 |
| Pages:
|
75-93 |
| . |
| Category:
|
math |
| . |
| Summary:
|
The notion of free group is defined, a relatively wide collection of groups which enable infinite set summation (called {\bf commutative $\pi$-group}), is introduced. Commutative $\pi$-groups are studied from the set-theoretical point of view and from the point of view of free groups. Commutativity of the operator which is a special kind of inverse limit and factorization, is proved. Tensor product is defined, commutativity of direct product (also a free group construction and tensor product) with the special kind of inverse limit is proved. Some important examples of tensor product are computed. (English) |
| Keyword:
|
alternative set theory |
| Keyword:
|
commutative $\pi $-group |
| Keyword:
|
free group |
| Keyword:
|
inverse system of Sd-classes and Sd-maps |
| Keyword:
|
prolongation |
| Keyword:
|
set-definable |
| Keyword:
|
tensor product |
| Keyword:
|
total homomorphism |
| MSC:
|
03E70 |
| MSC:
|
03H05 |
| MSC:
|
18G99 |
| MSC:
|
20F99 |
| MSC:
|
55N99 |
| idZBL:
|
Zbl 0735.03032 |
| idMR:
|
MR1118291 |
| . |
| Date available:
|
2008-10-09T13:11:07Z |
| Last updated:
|
2012-08-08 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/116944 |
| . |
| Related article:
|
http://dml.cz/handle/10338.dmlcz/118504 |
| Related article:
|
http://dml.cz/handle/10338.dmlcz/118551 |
| . |
| Reference:
|
[C] McCord M.C.: Non-standard analysis and homology.Fund. Math. 74 (1972), 21-28. Zbl 0233.55005, MR 0300270 |
| Reference:
|
[G] Garavaglia S.: Homology with equationally compact coefficients.Fund. Math. 100 (1978), 89-95. Zbl 0377.55006, MR 0494066 |
| Reference:
|
[E-S] Eilenberg S., Steenrod N.: Foundations of algebraic topology.Princeton Press, 1952. Zbl 0047.41402, MR 0050886 |
| Reference:
|
[H-W] Hilton P.J., Wylie S.: Homology Theory.Cambridge University Press, Cambridge, 1960. Zbl 0163.17803, 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. 128 (1987), 201-208. MR 0883385 |
| . |
