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

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

2004-04-20

arxiv.org/abs/math/0404372v1

Mathematics

General Topology

Scientific paper

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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