A factorization of metric spaces

Yoshito Ishiki

Published 2022-12-27Version 1

We first prove that for a metrizable space $X$, for a closed subset $F$ whose complement is zero-dimensional, the space $X$ can be embedded into a product space of the closed subset $F$ and a metrizable zero-dimensional space as a closed subset. Using this theorem, we next show the existence of extensors of metrics and ultrametrics, which preserve properties of metrics such as the completeness, the properness, being an ultrametrics, and its fractal dimensions This result contains some of the author's extension theorems of ultrametrics.