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Monotone properties defined from stars of open coverings

Authors
Journal
Topology and its Applications
0166-8641
Publisher
Elsevier
Volume
169
Identifiers
DOI: 10.1016/j.topol.2014.02.034
Keywords
  • Monotonically Star Closed-And-Discrete
  • Monotonically Star Finite
  • Non-Archimedean
  • Protometrizable
  • Paracompact Go-Space
  • Stationary Set
  • ω-Bounded
  • Sequentially Compact
  • [Formula Omitted]
  • Weak P-Point
  • Sorgenfrey Line
Disciplines
  • Mathematics

Abstract

Abstract We define some monotone properties using stars of coverings. This relates to work of J. van Mill, V. Tkachuk, R. Wilson, O. Alas, L. Junqueira, M. Matveev and others who generalized the D-space property of E. van Douwen and E. Michael. Given a property P, we call a topological space X monotonically star-P if one can assign to each open cover U a subspace s(U)⊆X with property P in such a way that st(s(U),U)=⋃{U∈U:U∩s(U)≠∅}=X and if V refines U then s(U)⊆s(V). We study monotonically star-P spaces for various compactness-like properties P.

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