Geodesic
An answer to a question of Arhangel'skii
Commentationes Mathematicae Universitatis Carolinae, Tome 42 (2001) no. 3, pp. 545-550 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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]).
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]).
Classification : 46E10, 54C35
Keywords: topology of pointwise convergence 
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     author = {Michalewski, Henryk},
     title = {An answer to a question of {Arhangel'skii}},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {545--550},
     year = {2001},
     volume = {42},
     number = {3},
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     zbl = {1053.54025},
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     url = {http://geodesic.mathdoc.fr/item/CMUC_2001_42_3_a12/}
}
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Michalewski, Henryk. An answer to a question of Arhangel'skii. Commentationes Mathematicae Universitatis Carolinae, Tome 42 (2001) no. 3, pp. 545-550. http://geodesic.mathdoc.fr/item/CMUC_2001_42_3_a12/