On the weak and pointwise topologies in function spaces II

Abstract

For a compact space $K$ we denote by $C_w(K)$ ($C_p(K)$) the space of continuous real-valued functions on $K$ endowed with the weak (pointwise) topology. In this paper we discuss the following basic question which seems to be open: Let $K$ and $L$ be infinite compact spaces. Can it happen that $C_w(K)$ and $C_p(L)$ are homeomorphic? M. Krupski proved that the above problem has a negative answer when $K=L$ and $K$ is finite-dimensional and metrizable. We extend this result to the class of finite-dimensional Valdivia compact spaces $K$.

References in corpus (1)

• The Ascoli property for function spaces and the weak topology of Banach and Fréchet spaces

Cited by in corpus (4)

• A countable dense homogeneous topological vector space is a Baire space
• On complemented copies of the space $c_0$ in spaces $C_p(X\times Y)$
• A note on Banach spaces $E$ admitting a continuous map from $C_p(X)$ onto $E_w$
• On linear continuous operators between distinguished spaces $C_p(X)$