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Homotopy theory, homological algebra, algebraic treatments of manifolds.

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deformation retraction of the complement

Let $X$ be a topological space and $V$ and $N$ are subspaces of $X$. It is known that if $V$ is homotopy equivalent to $N$ then $X-V$ need not be homotopy equivalent to $X-N$, the Alexander horned sp …
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