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Function spaces and local properties

Volume 223 / 2013

Ziqin Feng, Paul Gartside Fundamenta Mathematicae 223 (2013), 207-223 MSC: 54A25, 54B10, 54C05, 54D30. DOI: 10.4064/fm223-3-2


Necessary conditions and sufficient conditions are given for $C_p(X)$ to be a ($\sigma $-) $m_1$- or $m_3$-space. (A space is an $m_1$-space if each of its points has a closure-preserving local base.) A compact uncountable space $K$ is given with $C_{p}(K)$ an $m_1$-space, which answers questions raised by Dow, Ramírez Martínez and Tkachuk (2010) and Tkachuk (2011).


  • Ziqin FengDepartment of Mathematics
    Auburn University
    Auburn, AL 36830, U.S.A.
  • Paul GartsideDepartment of Mathematics
    University of Pittsburgh
    Pittsburgh, PA 15260, U.S.A.

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