# Homology theory in the alternative set theory I. Algebraic preliminaries

Commentationes Mathematicae Universitatis Carolinae (1991)

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

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topGuričan, 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

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- Živaljevič R.T., Infinitesimals, microsimplexes and elementary homology theory, AMM 93 (1986), 540-544. (1986) MR0856293
- Živaljevič R.T., On a cohomology theory based on hyperfinite sums of microsimplexes, Pacific J. Math. 128 (1987), 201-208. (1987) MR0883385

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