A short proof of a theorem of Morton Brown on chains of cells

Vladimir Uspenskij

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A short proof of a theorem of Morton Brown on chains of cells

Vladimir Uspenskij

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Abstract

Suppose that a topological space $X$ is the union of an increasing sequence of open subsets each of which is homeomorphic to the Euclidean space $R^n$. Then $X$ itself is homeomorphic to $R^n$. This is an old theorem of Morton Brown. We observe that this theorem is an immediate consequence of other two theorems of Morton Brown concerning near homeomorphisms and cellular sets.

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Vladimir Uspenskij. 2004-04-20. A short proof of a theorem of Morton Brown on chains of cells. https://arxiv.org/abs/math/0404372

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