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

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Given a homeomorphism on $\mathbb{R}^3$, can its effects on a compact subset be realized by ...

Let $f_1 \colon \mathbb{R}^3 \to \mathbb{R}^3$ be a homeomorphism, and let $K_1 \subseteq \mathbb{R}^3$ be compact. Does there always exist a homeomorphism $f_2 \colon \mathbb{R}^3 \to \mathbb{R}^3$ a …
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