Fixed points with respect to the L-slice homomorphism ${\sigma }_a$

Sabna, K.S., and Mangalambal, N.R.. "Fixed points with respect to the L-slice homomorphism $\sigma _{a} $." Archivum Mathematicum 055.1 (2019): 43-53. <http://eudml.org/doc/294862>.

@article{Sabna2019,
abstract = {Given a locale $L$ and a join semilattice $J$ with bottom element $0_\{J\}$, a new concept $(\sigma ,J)$ called $L$-slice is defined,where $\sigma $ is as an action of the locale $L$ on the join semilattice $J$. The $L$-slice $(\sigma ,J)$ adopts topological properties of the locale $L$ through the action $\sigma $. It is shown that for each $a\in L$, $\sigma _\{a\} $ is an interior operator on $(\sigma ,J)$.The collection $M=\lbrace \sigma _\{a\};a \in L\rbrace $ is a Priestly space and a subslice of $L$-$\operatorname\{Hom\}(J,J)$. If the locale $L$ is spatial we establish an isomorphism between the $L$-slices $(\sigma ,L) $ and $(\delta ,M) $. We have shown that the fixed set of $\sigma _\{a\}$, $a\in L $ is a subslice of $(\sigma ,J)$ and prove some equivalent properties.},
author = {Sabna, K.S., Mangalambal, N.R.},
journal = {Archivum Mathematicum},
keywords = {$L$-slice; $L$-slice homomorphism; subslice; fixed set and ideals},
language = {eng},
number = {1},
pages = {43-53},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Fixed points with respect to the L-slice homomorphism $\sigma _\{a\} $},
url = {http://eudml.org/doc/294862},
volume = {055},
year = {2019},
}

TY - JOUR
AU - Sabna, K.S.
AU - Mangalambal, N.R.
TI - Fixed points with respect to the L-slice homomorphism $\sigma _{a} $
JO - Archivum Mathematicum
PY - 2019
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 055
IS - 1
SP - 43
EP - 53
AB - Given a locale $L$ and a join semilattice $J$ with bottom element $0_{J}$, a new concept $(\sigma ,J)$ called $L$-slice is defined,where $\sigma $ is as an action of the locale $L$ on the join semilattice $J$. The $L$-slice $(\sigma ,J)$ adopts topological properties of the locale $L$ through the action $\sigma $. It is shown that for each $a\in L$, $\sigma _{a} $ is an interior operator on $(\sigma ,J)$.The collection $M=\lbrace \sigma _{a};a \in L\rbrace $ is a Priestly space and a subslice of $L$-$\operatorname{Hom}(J,J)$. If the locale $L$ is spatial we establish an isomorphism between the $L$-slices $(\sigma ,L) $ and $(\delta ,M) $. We have shown that the fixed set of $\sigma _{a}$, $a\in L $ is a subslice of $(\sigma ,J)$ and prove some equivalent properties.
LA - eng
KW - $L$-slice; $L$-slice homomorphism; subslice; fixed set and ideals
UR - http://eudml.org/doc/294862
ER -