Cauchy sequences in semimetric spaces

Author:
Dennis K. Burke

Journal:
Proc. Amer. Math. Soc. **33** (1972), 161-164

MSC:
Primary 54.30

DOI:
https://doi.org/10.1090/S0002-9939-1972-0290328-3

MathSciNet review:
0290328

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Abstract | References | Similar Articles | Additional Information

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 space *X* is semimetrizable if and only if it is a pseudo-open -image of a metric space.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1972-0290328-3

Keywords:
Semimetric space,
symmetric space,
Cauchy sequence,
weak condition of Cauchy,
developable space,
pseudo open map,
-map

Article copyright:
© Copyright 1972
American Mathematical Society