Connectifying a space by adding one point

M. R. Koushesh

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arXiv · 1701.00954

Connectifying a space by adding one point

M. R. Koushesh

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Abstract

It is a classical theorem of Alexandroff that a locally compact Hausdorff space has a one-point Hausdorff compactification if and only if it is non-compact. The one-point Hausdorff compactification is indeed obtained by adding the so called "point at infinity." Here we consider the analogous problem of existence of a one-point connectification, and keeping analogy, we prove that a locally connected normal space has a one-point normal connectification if and only if it has no compact component.

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BibTeX RIS

M. R. Koushesh. 2017-01-04. Connectifying a space by adding one point. https://arxiv.org/abs/1701.00954

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