We prove the following Main Theorem: Every continuous image of a Hausdorff topological space X is a generalized ordered space if and only if X is homeomorphic to a countable successor ordinal (with the order topology). This is a generalization of E. van Douwen's result about orderable spaces.
- Compact spaces
- Continuous images
- Generalized ordered topological spaces
- Linearly ordered topological spaces
ASJC Scopus subject areas
- Geometry and Topology