1. CMB 2008 (vol 51 pp. 570)
|Amsterdam Properties of $C_p(X)$ Imply Discreteness of $X$ |
We prove, among other things, that if $C_p(X)$ is subcompact in the sense of de Groot, then the space $X$ is discrete. This generalizes a series of previous results on completeness properties of function spaces.
Keywords:regular filterbase, subcompact space, function space, discrete space
Categories:54B10, 54C05, 54D30