Countable dense homogeneity of function spaces

Abstract

In this paper we consider the question of when the space Cp(X) of continuous real-valued functions on X with the pointwise convergence topology is countable dense homogeneous. In particular, we focus on the case when X is countable with a unique non-isolated point ∞. In this case, Cp(X) is countable dense homogeneous if and only if the filter of open neighborhoods of ∞ is a non-meager P -filter.