One-point connectifications of subspaces of the Euclidean line

Abstract

A connected Hausdorff space Y is called one-point connectification of a space X if X is embedded in Y and Y \ X has exactly one point. In this paper we characterize the subspaces of the Euclidean line which have a one-point connectification. Several examples are given to show how different is the situation in the Euclidean plane.

Keywords

• connected
• pathwise connected