Some remarks providing discontinuous maps on some $C_p(X)$ spaces
Volume 79 / 2008
Banach Center Publications 79 (2008), 131-133
MSC: 54C05, 54C35.
DOI: 10.4064/bc79-0-10
Abstract
Let $X$ be a completely regular Hausdorff topological space and $C_{p}(X)$ the space of continuous real-valued maps on $X$ endowed with the pointwise topology. A simple and natural argument is presented to show how to construct on the space $C_{p}(X)$, if $X$ contains a homeomorphic copy of the closed interval $[0,1]$, real-valued maps which are everywhere discontinuous but continuous on all compact subsets of $C_{p}(X)$.
