An answer to a question of Arhangel'skii

Michalewski, Henryk. "An answer to a question of Arhangel'skii." Commentationes Mathematicae Universitatis Carolinae 42.3 (2001): 545-550. <http://eudml.org/doc/248774>.

@article{Michalewski2001,
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 $C_p(X\times S) \lnot \approx _\{l\} C_p(X)$ where $S = (\lbrace 0\rbrace \cup \lbrace \frac\{1\}\{n+1\}:n\in \omega \rbrace )$ 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]).},
author = {Michalewski, Henryk},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {topology of pointwise convergence; function spaces; linear homeomorphisms},
language = {eng},
number = {3},
pages = {545-550},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {An answer to a question of Arhangel'skii},
url = {http://eudml.org/doc/248774},
volume = {42},
year = {2001},
}

TY - JOUR
AU - Michalewski, Henryk
TI - An answer to a question of Arhangel'skii
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2001
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 42
IS - 3
SP - 545
EP - 550
AB - 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 $C_p(X\times S) \lnot \approx _{l} C_p(X)$ where $S = (\lbrace 0\rbrace \cup \lbrace \frac{1}{n+1}:n\in \omega \rbrace )$ 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]).
LA - eng
KW - topology of pointwise convergence; function spaces; linear homeomorphisms
UR - http://eudml.org/doc/248774
ER -

References

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