Henriksen, Melvin, and Mitra, Biswajit. "$C(X)$ can sometimes determine $X$ without $X$ being realcompact." Commentationes Mathematicae Universitatis Carolinae 46.4 (2005): 711-720. <http://eudml.org/doc/249565>.
@article{Henriksen2005,
abstract = {As usual $C(X)$ will denote the ring of real-valued continuous functions on a Tychonoff space $X$. It is well-known that if $X$ and $Y$ are realcompact spaces such that $C(X)$ and $C(Y)$ are isomorphic, then $X$ and $Y$ are homeomorphic; that is $C(X)$determines$X$. The restriction to realcompact spaces stems from the fact that $C(X)$ and $C(\upsilon X)$ are isomorphic, where $\upsilon X$ is the (Hewitt) realcompactification of $X$. In this note, a class of locally compact spaces $X$ that includes properly the class of locally compact realcompact spaces is exhibited such that $C(X)$ determines $X$. The problem of getting similar results for other restricted classes of generalized realcompact spaces is posed.},
author = {Henriksen, Melvin, Mitra, Biswajit},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {nearly realcompact space; fast set; SRM ideal; continuous functions with pseudocompact support; locally compact; locally pseudocompact; nearly realcompact space; fast set; SRM ideal; continuous functions with pseudocompact support; locally compact},
language = {eng},
number = {4},
pages = {711-720},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {$C(X)$ can sometimes determine $X$ without $X$ being realcompact},
url = {http://eudml.org/doc/249565},
volume = {46},
year = {2005},
}
TY - JOUR
AU - Henriksen, Melvin
AU - Mitra, Biswajit
TI - $C(X)$ can sometimes determine $X$ without $X$ being realcompact
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2005
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 46
IS - 4
SP - 711
EP - 720
AB - As usual $C(X)$ will denote the ring of real-valued continuous functions on a Tychonoff space $X$. It is well-known that if $X$ and $Y$ are realcompact spaces such that $C(X)$ and $C(Y)$ are isomorphic, then $X$ and $Y$ are homeomorphic; that is $C(X)$determines$X$. The restriction to realcompact spaces stems from the fact that $C(X)$ and $C(\upsilon X)$ are isomorphic, where $\upsilon X$ is the (Hewitt) realcompactification of $X$. In this note, a class of locally compact spaces $X$ that includes properly the class of locally compact realcompact spaces is exhibited such that $C(X)$ determines $X$. The problem of getting similar results for other restricted classes of generalized realcompact spaces is posed.
LA - eng
KW - nearly realcompact space; fast set; SRM ideal; continuous functions with pseudocompact support; locally compact; locally pseudocompact; nearly realcompact space; fast set; SRM ideal; continuous functions with pseudocompact support; locally compact
UR - http://eudml.org/doc/249565
ER -
