First-countable spaces every quotient of which is orderable

Robert Bonnet, Arkady Leiderman

Research output: Contribution to journalArticlepeer-review


We prove the following Main Theorem: Every Hausdorff quotient image of a first-countable Hausdorff topological space X is a linearly ordered topological space (LOTS) if and only if X is a metrizable space which is the union of a discrete subspace and a compact countable subspace. As a corollary we characterize 1) σ-compact spaces, 2) locally compact spaces, 3) separable spaces every quotient image of which is a LOTS. We examine also several natural examples of non-first-countable Hausdorff topological spaces X such that every quotient image of X is a LOTS.

Original languageEnglish
Article number107478
JournalTopology and its Applications
StatePublished - 1 Feb 2021


  • Generalized ordered topological spaces
  • Linearly ordered topological spaces
  • Quotient mappings

ASJC Scopus subject areas

  • Geometry and Topology


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