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Keywords:
topology of pointwise convergence
topology of pointwise convergence
Summary:
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]).
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