2017/01/04 by M. R. Koushesh, Koushesh, M. R.
Engineering · #Architecture and Computational Design #FOS: Mathematics #General Topology (math.GN)
paper · pdf · doi:10.48550/arxiv.1701.00954
openalex publication_date 2017/01/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.