Further extending a complete convex metric

Author:
Robert A. Dooley

Journal:
Proc. Amer. Math. Soc. **40** (1973), 590-596

MSC:
Primary 54E50

DOI:
https://doi.org/10.1090/S0002-9939-1973-0322824-5

MathSciNet review:
0322824

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Abstract: A metric is convex if for every two points there is a third point such that . A generalized continuum is a connected, locally compact, metric space. Let be a nonempty space with a complete convex metric and let be a nonempty locally connected generalized continuum. The following condition is shown to be necessary and sufficient for there to exist a complete convex metric for that extends is a nonempty subspace of both and which is closed in and whose boundary is closed in .

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1973-0322824-5

Keywords:
Convex metric,
generalized continuum

Article copyright:
© Copyright 1973
American Mathematical Society