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

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Approximating an open bounded set by compact set

Let $U$ be an open bounded subset of $\mathbb{R}^n$, and $K$ a compact subset of $U$. Does there always exist a compact subset $L$ of $U$ that contains $K$, and such that $L$ is a retract of $U$. Loo …
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