Function spaces and local properties
Volume 223 / 2013
Fundamenta Mathematicae 223 (2013), 207-223
MSC: 54A25, 54B10, 54C05, 54D30.
DOI: 10.4064/fm223-3-2
Abstract
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).
