In homotopy theory we identify maps that are homotopic. For two mappings from $X$ to $Y$ we look for subspaces of $X$ on which they are homotopic. The minimum number of such subspaces covering the domain $X$ is declared to be their homotopic distance. Using properties of homotopy and extending the covers of normal spaces, we prove that the homotopic distance on them is a metric.
We connect homotopic distance with Lusternik-Schnirelmann category and topological complexity. The links between them simplify the proofs of their properties and present them in a new light.
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