On Spaces Star Determined by Compact Metrizable Subspaces

  • Wei-Feng XuanEmail author
  • Yan-Kui Song
Original Paper


A space X is said to be star determined by compact metrizable subspaces (star-CM for short) if for any open cover \({\mathcal {U}}\) of X there is a compact and metrizable subspace \(Y \subset X\) such that \({\text {St}}(Y, {\mathcal {U}})=X\). This notation of star-CM was introduced by van Mill, Tkachuk and Wilson in (Topol Appl 154:2127–2134, 2007). In this paper, we investigate the relations between star-CM spaces and related spaces, and study topological properties of star-CM spaces. We also establish a cardinal theorem for star-CM spaces with symmetric g-functions.


Star-CM Star countable Star compact g-Function 

Mathematics Subject Classification

54D20 54E35 



We would like to thank the referee for his (or her) valuable remarks and suggestions which greatly improved the paper.


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Copyright information

© Iranian Mathematical Society 2019

Authors and Affiliations

  1. 1.School of statistics and MathematicsNanjing Audit UniversityNanjingChina
  2. 2.Institute of Mathematics, School of Mathematical ScienceNanjing Normal UniversityNanjingChina

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