Homology theory in the AST II. Basic concepts, Eilenberg-Steenrod's axioms

Jaroslav Guričan

Commentationes Mathematicae Universitatis Carolinae (1992)

  • Volume: 33, Issue: 2, page 353-372
  • ISSN: 0010-2628

Abstract

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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.

How to cite

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Guričan, Jaroslav. "Homology theory in the AST II. Basic concepts, Eilenberg-Steenrod's axioms." Commentationes Mathematicae Universitatis Carolinae 33.2 (1992): 353-372. <http://eudml.org/doc/247415>.

@article{Guričan1992,
abstract = {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.},
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; Eilenberg-Steenrod axioms; AST; indiscernibility relations},
language = {eng},
number = {2},
pages = {353-372},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Homology theory in the AST II. Basic concepts, Eilenberg-Steenrod's axioms},
url = {http://eudml.org/doc/247415},
volume = {33},
year = {1992},
}

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
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 33
IS - 2
SP - 353
EP - 372
AB - 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.
LA - eng
KW - alternative set theory; set-definable; homology theory; simplex; complex; Sd-IS of groups; Alternative Set Theory; Eilenberg-Steenrod axioms; AST; indiscernibility relations
UR - http://eudml.org/doc/247415
ER -

References

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  4. Garavaglia S., Homology with equationally compact coefficients, Fund. Math. 100 (1978), 89-95. (1978) Zbl0377.55006MR0494066
  5. Guričan J., Homology theory in the alternative set theory I. Algebraic preliminaries., Comment. Math. Univ. Carolinae 32 (1991), 75-93. (1991) MR1118291
  6. Guričan J., Zlatoš P., Archimedean and geodetical biequivalences, Comment. Math. Univ. Carolinae 26 (1985), 675-698. (1985) MR0831804
  7. Hilton P.J., Wylie S., Homology Theory, Cambridge University Press Cambridge (1960). (1960) Zbl0091.36306MR0115161
  8. Sochor A., Vopěnka P., Endomorphic universes and their standard extensions, Comment. Math. Univ. Carolinae 20 (1979), 605-629. (1979) MR0555178
  9. Vopěnka P., Mathematics in the Alternative Set Theory, Teubner-Texte Leipzig (1979). (1979) MR0581368
  10. Vopěnka P., Mathematics in the Alternative Set Theory, (in Slovak) ALFA Bratislava (1989). (1989) 
  11. Wattenberg F., Non-standard analysis and the theory of shape, Fund. Math. 98 (1978), 41-60. (1978) MR0528354
  12. Živaljevič R.T., Infinitesimals, microsimplexes and elementary homology theory, AMM 93 (1986), 540-544. (1986) MR0856293
  13. Živaljevič R.T., On a cohomology theory based on hyperfinite sums of microsimplexes, Pacific J. Math. (1987), 128 201-208. (1987) MR0883385

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