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arXiv · 0710.0080

Equivalent metrics and compactifications

Young Deuk Kim
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Abstract

Let (X,d) be a metric space and m\in X. Suppose that ϕ:X\times X\to\mathbold{R} is a nonnegative symmetric function. We define a metric d^{ϕ,m} on X which is equivalent to d. If d^{ϕ,m} is totally bounded, its completion is a compactification of (X,d). As examples, we construct two compactifications of (\mathhbold{R}^s,d_E), where d_E is the Euclidean metric and s\geq 2.

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BibTeXRIS

Young Deuk Kim. 2007-09-29. Equivalent metrics and compactifications. https://arxiv.org/abs/0710.0080

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