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The Canonical Induced Metric for Topological Branched Coverings and Geometric Applications
Given a continuous map $f:X\to Y$ from a continuum-connected space into a metric space, we introduce an associated canonical pullback metric $d_f$ on $X$ by combining the target diameter structure with the Mazurkiewicz construction as \[ d_f(x,x')=\inf\{\operatorname{diam}_Y f(E): E\subset X\tex
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