| Title:
|
Locally functionally countable subalgebra of $\mathcal{R}(L)$ (English) |
| Author:
|
Elyasi, M. |
| Author:
|
Estaji, A. A. |
| Author:
|
Robat Sarpoushi, M. |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
56 |
| Issue:
|
3 |
| Year:
|
2020 |
| Pages:
|
127-140 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $L_c(X)= \lbrace f \in C(X) \colon \overline{C_f}= X\rbrace $, where $C_f$ is the union of all open subsets $U \subseteq X$ such that $\vert f(U) \vert \le \aleph _0$. In this paper, we present a pointfree topology version of $L_c(X)$, named $\mathcal{R}_{\ell c}(L)$. We observe that $\mathcal{R}_{\ell c}(L)$ enjoys most of the important properties shared by $\mathcal{R}(L)$ and $\mathcal{R}_c(L)$, where $\mathcal{R}_c(L)$ is the pointfree version of all continuous functions of $C(X)$ with countable image. The interrelation between $\mathcal{R}(L)$, $\mathcal{R}_{\ell c}(L)$, and $\mathcal{R}_c(L)$ is examined. We show that $L_c(X) \cong \mathcal{R}_{\ell c}\big (\mathfrak{O}(X)\big )$ for any space $X$. Frames $L$ for which $\mathcal{R}_{\ell c}(L)=\mathcal{R}(L)$ are characterized. (English) |
| Keyword:
|
functionally countable subalgebra |
| Keyword:
|
locally functionally countable subalgebra |
| Keyword:
|
sublocale |
| Keyword:
|
frame |
| MSC:
|
06D22 |
| MSC:
|
54C05 |
| MSC:
|
54C30 |
| idZBL:
|
Zbl 07250674 |
| idMR:
|
MR4156440 |
| DOI:
|
10.5817/AM2020-3-127 |
| . |
| Date available:
|
2020-09-02T08:48:26Z |
| Last updated:
|
2020-11-23 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/148290 |
| . |
| Reference:
|
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