Henryk Michalewski
An answer to a question of Arhangel'skii

Comment.Math.Univ.Carolinae 42,3 (2001) 545-550.

Abstract:We prove that there exists an example of a metrizable non-discrete space $X$, such that $C_p(X\times \omega )\approx _{l} C_p(X)$ but $C_p(X\times S) \not \approx _{l} C_p(X)$ where $S = (\{0\}\cup \{\frac {1}{n+1}:n\in \omega \})$ and $C_p(X)$ is the space of all continuous functions from $X$ into reals equipped with the topology of pointwise convergence. It answers a question of Arhangel'skii ([2, Problem 4]).

Keywords: topology of pointwise convergence
AMS Subject Classification: Primary 54C35