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A factorization of metric spaces

Yoshito Ishiki
Dec 2022
摘要
We first prove that for a metrizable space $X$, for a closed subset $F$ whosecomplement is zero-dimensional, the space $X$ can be embedded into a productspace of the closed subset $F$ and a metrizable zero-dimensional space as aclosed subset. Using this theorem, we next show the existence of extensors ofmetrics and ultrametrics, which preserve properties of metrics such as thecompleteness, the properness, being an ultrametrics, and its fractal dimensionsThis result contains some of the author's extension theorems of ultrametrics.
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