Homology theory in the alternative set theory I. Algebraic preliminaries

Jaroslav Guričan

Commentationes Mathematicae Universitatis Carolinae (1991)

  • Volume: 32, Issue: 1, page 75-93
  • ISSN: 0010-2628

Abstract

top
The notion of free group is defined, a relatively wide collection of groups which enable infinite set summation (called commutative π -group), is introduced. Commutative π -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.

How to cite

top

Guričan, Jaroslav. "Homology theory in the alternative set theory I. Algebraic preliminaries." Commentationes Mathematicae Universitatis Carolinae 32.1 (1991): 75-93. <http://eudml.org/doc/247248>.

@article{Guričan1991,
abstract = {The notion of free group is defined, a relatively wide collection of groups which enable infinite set summation (called 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.},
author = {Guričan, Jaroslav},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {alternative set theory; commutative $\pi $-group; free group; inverse system of Sd-classes and Sd-maps; prolongation; set-definable; tensor product; total homomorphism; commutative -group; inverse system of -classes and -maps; tensor product; prolongation; homology theory; alternative set theory},
language = {eng},
number = {1},
pages = {75-93},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Homology theory in the alternative set theory I. Algebraic preliminaries},
url = {http://eudml.org/doc/247248},
volume = {32},
year = {1991},
}

TY - JOUR
AU - Guričan, Jaroslav
TI - Homology theory in the alternative set theory I. Algebraic preliminaries
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1991
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 32
IS - 1
SP - 75
EP - 93
AB - The notion of free group is defined, a relatively wide collection of groups which enable infinite set summation (called 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.
LA - eng
KW - alternative set theory; commutative $\pi $-group; free group; inverse system of Sd-classes and Sd-maps; prolongation; set-definable; tensor product; total homomorphism; commutative -group; inverse system of -classes and -maps; tensor product; prolongation; homology theory; alternative set theory
UR - http://eudml.org/doc/247248
ER -

References

top
  1. McCord M.C., Non-standard analysis and homology, Fund. Math. 74 (1972), 21-28. (1972) Zbl0233.55005MR0300270
  2. Garavaglia S., Homology with equationally compact coefficients, Fund. Math. 100 (1978), 89-95. (1978) Zbl0377.55006MR0494066
  3. Eilenberg S., Steenrod N., Foundations of algebraic topology, Princeton Press, 1952. Zbl0047.41402MR0050886
  4. Hilton P.J., Wylie S., Homology Theory, Cambridge University Press, Cambridge, 1960. Zbl0163.17803MR0115161
  5. Sochor A., Vopěnka P., Endomorphic universes and their standard extensions, Comment. Math. Univ. Carolinae 20 (1979), 605-629. (1979) MR0555178
  6. Vopěnka P., Mathematics in the alternative set theory, Teubner-Texte, Leipzig, 1979. MR0581368
  7. Vopěnka P., Mathematics in the alternative set theory (in Slovak), Alfa, Bratislava, 1989. 
  8. Wattenberg F., Non-standard analysis and the theory of shape, Fund. Math. 98 (1978), 41-60. (1978) MR0528354
  9. Živaljevič R.T., Infinitesimals, microsimplexes and elementary homology theory, AMM 93 (1986), 540-544. (1986) MR0856293
  10. Živaljevič R.T., On a cohomology theory based on hyperfinite sums of microsimplexes, Pacific J. Math. 128 (1987), 201-208. (1987) MR0883385

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.