Homology theory in the AST II. Basic concepts, Eilenberg-Steenrod's axioms
Commentationes Mathematicae Universitatis Carolinae, Tome 33 (1992) no. 2, pp. 353-372 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

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.
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.
Classification : 03E70, 03H05, 55N35
Keywords: alternative set theory; set-definable; homology theory; simplex; complex; Sd-IS of groups
@article{CMUC_1992_33_2_a16,
     author = {Guri\v{c}an, Jaroslav},
     title = {Homology theory in the {AST} {II.} {Basic} concepts, {Eilenberg-Steenrod's} axioms},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {353--372},
     year = {1992},
     volume = {33},
     number = {2},
     mrnumber = {1189667},
     zbl = {0761.55004},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMUC_1992_33_2_a16/}
}
TY  - JOUR
AU  - Guričan, Jaroslav
TI  - Homology theory in the AST II. Basic concepts, Eilenberg-Steenrod's axioms
JO  - Commentationes Mathematicae Universitatis Carolinae
PY  - 1992
SP  - 353
EP  - 372
VL  - 33
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/CMUC_1992_33_2_a16/
LA  - en
ID  - CMUC_1992_33_2_a16
ER  - 
%0 Journal Article
%A Guričan, Jaroslav
%T Homology theory in the AST II. Basic concepts, Eilenberg-Steenrod's axioms
%J Commentationes Mathematicae Universitatis Carolinae
%D 1992
%P 353-372
%V 33
%N 2
%U http://geodesic.mathdoc.fr/item/CMUC_1992_33_2_a16/
%G en
%F CMUC_1992_33_2_a16
Guričan, Jaroslav. Homology theory in the AST II. Basic concepts, Eilenberg-Steenrod's axioms. Commentationes Mathematicae Universitatis Carolinae, Tome 33 (1992) no. 2, pp. 353-372. http://geodesic.mathdoc.fr/item/CMUC_1992_33_2_a16/

[A] Alexandrov P.S.: Combinatorial Topology. Moskva (1947),(in Russian).

[C] Cord M.C.: Non-standard analysis and homology. Fund. Math. 74 (1972), 21-28. | MR

[E-S] Eilenberg S., Steenrod N.: Foundations of Algebraic Topology. Princeton Press (1952). | MR | Zbl

[G] Garavaglia S.: Homology with equationally compact coefficients. Fund. Math. 100 (1978), 89-95. | MR | Zbl

[G1] Guričan J.: Homology theory in the alternative set theory I. Algebraic preliminaries. Comment. Math. Univ. Carolinae 32 (1991), 75-93. | MR

[G-Z] Guričan J., Zlatoš P.: Archimedean and geodetical biequivalences. Comment. Math. Univ. Carolinae 26 (1985), 675-698. | MR

[H-W] Hilton P.J., Wylie S.: Homology Theory. Cambridge University Press Cambridge (1960). | MR | Zbl

[S-V] Sochor A., Vopěnka P.: Endomorphic universes and their standard extensions. Comment. Math. Univ. Carolinae 20 (1979), 605-629. | MR

[V1] Vopěnka P.: Mathematics in the Alternative Set Theory. Teubner-Texte Leipzig (1979). | MR

[V2] Vopěnka P.: Mathematics in the Alternative Set Theory. (in Slovak) ALFA Bratislava (1989).

[W] Wattenberg F.: Non-standard analysis and the theory of shape. Fund. Math. 98 (1978), 41-60. | MR

[Ž1] Živaljevič R.T.: Infinitesimals, microsimplexes and elementary homology theory. AMM 93 (1986), 540-544. | MR

[Ž2] Živaljevič R.T.: On a cohomology theory based on hyperfinite sums of microsimplexes. Pacific J. Math. (1987), 128 201-208. | MR