## 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

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