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Property (G), Regularity, and Semi-Equicontinuity

Published online by Cambridge University Press:  20 November 2018

J. S. Yang
J. S. Yang*
Affiliation:
University of South Carolina, Columbia, South Carolina
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This note, motivated by [2], [3], and [4], is devoted to an investigation of properties related to equicontinuity in function spaces of topological spaces. In §2, we study the property (G) defined in [3], and the regularity defined in [4]. A sufficient condition for the simultaneous continuity of a function of two variables, which is analogous to a well known result in equicontinuity, is given at the end of the section. In §3, we relate the regularity with the semi-equicontinuity defined in [2], by localizing the semi-equicontinuity in an obvious way which leads us to weaken some of the hypotheses used in [2]. By the way of constructing an example, we also obtained a sufficient condition for a regular semitopological group to be a topological group.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 16 , Issue 4 , December 1973 , pp. 587 - 594
Copyright
Copyright © Canadian Mathematical Society 1973

References

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