TY - JOUR

T1 - First-countable spaces every quotient of which is orderable

AU - Bonnet, Robert

AU - Leiderman, Arkady

N1 - Publisher Copyright:
© 2020 Elsevier B.V.

PY - 2021/2/1

Y1 - 2021/2/1

N2 - 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.

AB - 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.

KW - Generalized ordered topological spaces

KW - Linearly ordered topological spaces

KW - Quotient mappings

UR - http://www.scopus.com/inward/record.url?scp=85097046144&partnerID=8YFLogxK

U2 - 10.1016/j.topol.2020.107478

DO - 10.1016/j.topol.2020.107478

M3 - Article

AN - SCOPUS:85097046144

SN - 0166-8641

VL - 288

JO - Topology and its Applications

JF - Topology and its Applications

M1 - 107478

ER -