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

Jaroslav Guričan

Displaying similar documents to “Homology theory in the AST III. Comparison with homology theories of Čech and Vietoris”

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

Jaroslav Guričan (1992)

Commentationes Mathematicae Universitatis Carolinae

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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.

Homology theory in the alternative set theory I. Algebraic preliminaries

Jaroslav Guričan (1991)

Commentationes Mathematicae Universitatis Carolinae

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The notion of free group is defined, a relatively wide collection of groups which enable infinite set summation (called ), 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...

Absolutely continuous functions of several variables and diffeomorphisms

Stanislav Hencl, Jan Malý (2003)

Open Mathematics

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In [4], a class of absolutely continuous functions of d-variables, motivated by applications to change of variables in an integral, has been introduced. The main result of this paper states that absolutely continuous functions in the sense of [4] are not stable under diffeomorphisms. We also show an example of a function which is absolutely continuous with respect cubes but not with respect to balls.