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Metrization of Topological Spaces

Published online by Cambridge University Press:  20 November 2018

R. H. Bing
R. H. Bing*
Affiliation:
University of Virginia and University of Wisconsin
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A single valued function D(x, y) is a metric for a topological space provided that for points x, y, z of the space:

1. D(x, y) ≽ 0, the equality holding if and only if x = y,

2. D(x, y) = D(y, x) (symmetry),

3. D(x, y) + D(y, z) ≽ D(x, z) (triangle inequality),

4. x belongs to the closure of the set M if and only if D(x, m) (m element of M) is not bounded from 0 (preserves limit points).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 3 , 1951 , pp. 175 - 186
Copyright
Copyright © Canadian Mathematical Society 1951

References

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