Cauchy sequences in semimetric spaces-Reference-Cited by-同舟云学术

Cauchy sequences in semimetric spaces

Published:1972 Issue:1 Volume:33 Page:161-164
ISSN:0002-9939
Container-title:Proceedings of the American Mathematical Society
language:en
Short-container-title:Proc. Amer. Math. Soc.

Author:

Burke Dennis K.

Abstract

As the main result we prove that every semimetrizable space has a semimetric for which every convergent sequence has a Cauchy subsequence. This result is used to show that a T 1 {T_1} space X is semimetrizable if and only if it is a pseudo-open π \pi -image of a metric space.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/proc/1972-033-01/S0002-9939-1972-0290328-3/S0002-9939-1972-0290328-3.pdf

Reference9 articles.

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4. Semi-metric functions and semi-metric spaces;Bennett, H. R.,1970

5. Morton Brown, Semi-metric spaces, Summer Institute on Set Theoretic Topology, Madison, Wisconsin, Amer. Math. Soc., Providence, R.I., 1955, pp. 62-64.

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