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DENSITY, SMITAL PROPERTY AND QUASICONTINUITY

Part of: Classical measure theory Topological and differentiable algebraic systems

Published online by Cambridge University Press:  04 December 2017

GRAŻYNA HORBACZEWSKA Open the ORCID record for GRAŻYNA HORBACZEWSKA [Opens in a new window]  and
SEBASTIAN LINDNER
GRAŻYNA HORBACZEWSKA*
Affiliation:
Department of Mathematics and Computer Science, University of Lodz, Banacha 22, 90 238 Lodz, Poland email [email protected]
SEBASTIAN LINDNER
Affiliation:
Department of Mathematics and Computer Science, University of Lodz, Banacha 22, 90 238 Lodz, Poland email [email protected]
*
✉[email protected]
Rights & Permissions [Opens in a new window]

Abstract

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Based on the abstract version of the Smital property, we introduce an operator $DS$. We use it to characterise the class of semitopological abelian groups, for which addition is a quasicontinuous operation.

Keywords

quasicontinuitySmital lemmasemitopological groups

MSC classification

Primary: 22A30: Other topological algebraic systems and their representations
Secondary: 28A05: Classes of sets (Borel fields, $sigma$-rings, etc.), measurable sets, Suslin sets, analytic sets
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 97 , Issue 2 , April 2018 , pp. 246 - 252
Copyright
© 2017 Australian Mathematical Publishing Association Inc. 

References

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