Connectedness of some rings of quotients of with the -topology
F. Azarpanah; M. Paimann; A. R. Salehi
Commentationes Mathematicae Universitatis Carolinae (2015)
- Volume: 56, Issue: 1, page 63-76
- ISSN: 0010-2628
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topAzarpanah, F., Paimann, M., and Salehi, A. R.. "Connectedness of some rings of quotients of $C(X)$ with the $m$-topology." Commentationes Mathematicae Universitatis Carolinae 56.1 (2015): 63-76. <http://eudml.org/doc/269891>.
@article{Azarpanah2015,
abstract = {In this article we define the $m$-topology on some rings of quotients of $C(X)$. Using this, we equip the classical ring of quotients $q(X)$ of $C(X)$ with the $m$-topology and we show that $C(X)$ with the $r$-topology is in fact a subspace of $q(X)$ with the $m$-topology. Characterization of the components of rings of quotients of $C(X)$ is given and using this, it turns out that $q(X)$ with the $m$-topology is connected if and only if $X$ is a pseudocompact almost $P$-space, if and only if $C(X)$ with $r$-topology is connected. We also observe that the maximal ring of quotients $Q(X)$ of $C(X)$ with the $m$-topology is connected if and only if $X$ is finite. Finally for each point $x$, we introduce a natural ring of quotients of $C(X)/O_x$ which is connected with the $m$-topology.},
author = {Azarpanah, F., Paimann, M., Salehi, A. R.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {$r$-topology; $m$-topology; almost $P$-space; pseudocompact space; component; classical ring of quotients of $C(X)$; -topology; -topology; almost -space; pseudocompact space; ring of quotients of $C(X)$},
language = {eng},
number = {1},
pages = {63-76},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Connectedness of some rings of quotients of $C(X)$ with the $m$-topology},
url = {http://eudml.org/doc/269891},
volume = {56},
year = {2015},
}
TY - JOUR
AU - Azarpanah, F.
AU - Paimann, M.
AU - Salehi, A. R.
TI - Connectedness of some rings of quotients of $C(X)$ with the $m$-topology
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2015
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 56
IS - 1
SP - 63
EP - 76
AB - In this article we define the $m$-topology on some rings of quotients of $C(X)$. Using this, we equip the classical ring of quotients $q(X)$ of $C(X)$ with the $m$-topology and we show that $C(X)$ with the $r$-topology is in fact a subspace of $q(X)$ with the $m$-topology. Characterization of the components of rings of quotients of $C(X)$ is given and using this, it turns out that $q(X)$ with the $m$-topology is connected if and only if $X$ is a pseudocompact almost $P$-space, if and only if $C(X)$ with $r$-topology is connected. We also observe that the maximal ring of quotients $Q(X)$ of $C(X)$ with the $m$-topology is connected if and only if $X$ is finite. Finally for each point $x$, we introduce a natural ring of quotients of $C(X)/O_x$ which is connected with the $m$-topology.
LA - eng
KW - $r$-topology; $m$-topology; almost $P$-space; pseudocompact space; component; classical ring of quotients of $C(X)$; -topology; -topology; almost -space; pseudocompact space; ring of quotients of $C(X)$
UR - http://eudml.org/doc/269891
ER -
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