| Title:
|
Fixed points with respect to the L-slice homomorphism $\sigma _{a} $ (English) |
| Author:
|
Sabna, K.S. |
| Author:
|
Mangalambal, N.R. |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
55 |
| Issue:
|
1 |
| Year:
|
2019 |
| Pages:
|
43-53 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
$L$-slice |
| Keyword:
|
$L$-slice homomorphism |
| Keyword:
|
subslice |
| Keyword:
|
fixed set and ideals |
| MSC:
|
03G10 |
| MSC:
|
06A12 |
| MSC:
|
06D22 |
| idZBL:
|
Zbl 07088757 |
| idMR:
|
MR3939063 |
| DOI:
|
10.5817/AM2019-1-43 |
| . |
| Date available:
|
2019-03-23T12:22:03Z |
| Last updated:
|
2020-02-27 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/147649 |
| . |
| Reference:
|
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| . |
