Homology theory in the AST III. Comparison with homology theories of Čech and Vietoris

Jaroslav Guričan

Commentationes Mathematicae Universitatis Carolinae (1993)

  • Volume: 34, Issue: 1, page 11-22
  • ISSN: 0010-2628

Abstract

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The isomorphism between our homology functor and these of Vietoris and Čech is proved. Introductory result on dimension is proved.

How to cite

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Guričan, Jaroslav. "Homology theory in the AST III. Comparison with homology theories of Čech and Vietoris." Commentationes Mathematicae Universitatis Carolinae 34.1 (1993): 11-22. <http://eudml.org/doc/247509>.

@article{Guričan1993,
abstract = {The isomorphism between our homology functor and these of Vietoris and Čech is proved. Introductory result on dimension is proved.},
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; set-definable; homology theory; simplex; complex; Sd-IS of groups},
language = {eng},
number = {1},
pages = {11-22},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Homology theory in the AST III. Comparison with homology theories of Čech and Vietoris},
url = {http://eudml.org/doc/247509},
volume = {34},
year = {1993},
}

TY - JOUR
AU - Guričan, Jaroslav
TI - Homology theory in the AST III. Comparison with homology theories of Čech and Vietoris
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1993
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 34
IS - 1
SP - 11
EP - 22
AB - The isomorphism between our homology functor and these of Vietoris and Čech is proved. Introductory result on dimension is proved.
LA - eng
KW - alternative set theory; set-definable; homology theory; simplex; complex; Sd-IS of groups; alternative set theory; set-definable; homology theory; simplex; complex; Sd-IS of groups
UR - http://eudml.org/doc/247509
ER -

References

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  3. Dowker C.H., Homology groups of relations, Ann. Math 56 (1952), 84-95. (1952) Zbl0046.40402MR0048030
  4. Eilenberg S., Steenrod N., Foundations of Algebraic Topology, Princeton Press (1952). (1952) Zbl0047.41402MR0050886
  5. Garavaglia S., Homology with equationally compact coefficients, Fund. Math. 100 (1978), 89-95. (1978) Zbl0377.55006MR0494066
  6. Guričan J., Homology theory in the alternative set theory I. Algebraic preliminaries., Comment. Math. Univ. Carolinae 32 (1991), 75-93. (1991) MR1118291
  7. Guričan J., Homology theory in the AST II. Basic concepts, Eilenberg-Steenrod's axioms, Comment. Math. Univ. Carolinae 33 (1992), 353-372. (1992) Zbl0761.55004MR1189667
  8. Hilton P.J., Wylie S., Homology Theory, Cambridge University Press Cambridge (1960). (1960) Zbl0091.36306MR0115161
  9. Sochor A., Vopěnka P., Endomorphic universes and their standard extensions, Comment. Math. Univ. Carolinae 20 (1979), 605-629. (1979) MR0555178
  10. Sgall J., Witzany J., Dimension of indiscernibility equivalences, Comment. Math. Univ. Carolinae 28 (1987), 537-547. (1987) Zbl0629.03034MR0912582
  11. Vopěnka P., Mathematics in the Alternative Set Theory, Teubner-Texte Leipzig (1979). (1979) MR0581368
  12. Vopěnka P., Introduction to Mathematics in the Alternative Set Theory (in Slovak), ALFA Bratislava (1989). (1989) 
  13. Wattenberg F., Non-standard analysis and the Theory of shape, Fund. Math. 98 (1978), 41-60. (1978) MR0528354
  14. Živaljevič R.T., Infinitesimals, microsimplexes and elementary homology theory, AMM 7 (1986), 540-544. (1986) MR0856293
  15. Živaljevič R.T., On a cohomology theory based on hyperfinite sums of microsimplexes, Pacific J. Math. (1987), 1 201-208. (1987) MR0883385

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