Displaying similar documents to “Regular and Other Kinds of Extensions of Topological Spaces”

On extension of the group operation over the Čech-Stone compactification

Jan Jełowicki (1993)

Colloquium Mathematicae

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The convolution of ultrafilters of closed subsets of a normal topological group is considered as a substitute of the extension onto ( β ) 2 of the group operation. We find a subclass of ultrafilters for which this extension is well-defined and give some examples of pathologies. Next, for a given locally compact group and its dense subgroup , we construct subsets of β algebraically isomorphic to . Finally, we check whether the natural mapping from β onto β is a homomorphism with respect to...

Completely regular spaces

H. L. Bentley, Eva Lowen-Colebunders (1991)

Commentationes Mathematicae Universitatis Carolinae

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We conduct an investigation of the relationships which exist between various generalizations of complete regularity in the setting of merotopic spaces, with particular attention to filter spaces such as Cauchy spaces and convergence spaces. Our primary contribution consists in the presentation of several counterexamples establishing the divergence of various such generalizations of complete regularity. We give examples of: (1) a contigual zero space which is not weakly regular and is...

Regular and biregular functions in the sense of Fueter - some problems

W. Królikowski, R. Michael Porter (1994)

Annales Polonici Mathematici

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The biregular functions in the sense of Fueter are investigated. In particular, the class of LR-biregular mappings (left regular with a right regular inverse) is introduced. Moreover, the existence of non-affine biregular mappings is established via examples. Some applications to the quaternionic manifolds are given.

A linear extension operator for Whitney fields on closed o-minimal sets

Wiesław Pawłucki (2008)

Annales de l’institut Fourier

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A continuous linear extension operator, different from Whitney’s, for 𝒞 p -Whitney fields (p finite) on a closed o-minimal subset of ℝ n is constructed. The construction is based on special geometrical properties of o-minimal sets earlier studied by K. Kurdyka with the author.

Measures of compactness in approach spaces

R. Baekeland, Robert Lowen (1995)

Commentationes Mathematicae Universitatis Carolinae

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We investigate whether in the setting of approach spaces there exist measures of relative compactness, (relative) sequential compactness and (relative) countable compactness in the same vein as Kuratowski's measure of compactness. The answer is yes. Not only can we prove that such measures exist, but we can give usable formulas for them and we can prove that they behave nicely with respect to each other in the same way as the classical notions.