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Continuum theory, point-set topology, spaces with algebraic structure, foundations, dimension theory, local and global properties.

4 votes
1 answer
1k views

A boundary-preserving map on the unit disk

We are given a (closed) ball $D^n$ and a (continuous) map $f: D^n \to D^n$, that is identity on the boundary of $D^n$. Let $C$ be a subset of $D^n$, and let $f^{-1}(C)$ be the inverse image of $C$ i …