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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

1. Ezust, Paul, Joint continuity of function spaces, Colloq. Math. 21 (1970), 87–89.Google Scholar
2. Fuller, R. V., Semiuniform spaces and topological homeomorphism groups, Proc. Amer. Math. Soc. 26 (1970), 365–368.Google Scholar
3. Gale, D., Compact sets of functions and function rings, Proc. Amer. Math. Soc. 1 (1950), 303–308.Google Scholar
4. Kaul, S. K., Compact subsets in function spaces, Canad. Math. Bull. 12 (1969), 461–466.Google Scholar
5. Kelley, J. L., General topology, Van Nostrand, Princeton, N.J., 1955.Google Scholar
6. Weston, J. D., A generalization of Ascoli’s theorem, Mathematika, 6 (1959), 19–24.Google Scholar