A characterization of the connectivity of a manifold in terms of large open cells

Summerhill, R. Richard

doi:10.1090/S0002-9939-1974-0380808-6

A characterization of the connectivity of a manifold in terms of large open cells
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Proc. Amer. Math. Soc. 45 (1974), 285-290 Request permission

Abstract:

If $k$ and $n$ are integers, $0 \leqslant k \leqslant n - 3$, and ${M^n}$ is a topological $n$-manifold without boundary, it is shown that $M$ is $k$-connected if and only if there is a “tame” $(n - k - 1)$-dimensional closed subset $X$ in $M$ such that $M - X$ is homeomorphic to ${E^n}$.

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