Countable successor ordinals as generalized ordered topological spaces

Abstract

We prove the following Main Theorem: Assume that any continuous image of a Hausdorff topological space X is a generalized ordered space. Then X is homeomorphic to a countable successor ordinal (with the order topology). The converse trivially holds.Date: December 26, 2016. 1991 Mathematics Subject Classification. 03E10, 06A05, 54F05, 54F65.