| Title:
|
The (dis)connectedness of products of Hausdorff spaces in the box topology (English) |
| Author:
|
Chatyrko, Vitalij A. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
62 |
| Issue:
|
4 |
| Year:
|
2021 |
| Pages:
|
483-489 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper the following two propositions are proved: (a) If $X_\alpha$, $\alpha \in A$, is an infinite system of connected spaces such that infinitely many of them are nondegenerated completely Hausdorff topological spaces then the box product $\square_{\alpha \in A} X_\alpha$ can be decomposed into continuum many disjoint nonempty open subsets, in particular, it is disconnected. (b) If $X_\alpha$, $\alpha \in A$, is an infinite system of Brown Hausdorff topological spaces then the box product $\square_{\alpha \in A} X_\alpha$ is also Brown Hausdorff, and hence, it is connected. A space is Brown if for every pair of its open nonempty subsets there exists a point common to their closures. There are many examples of countable Brown Hausdorff spaces in literature. (English) |
| Keyword:
|
box topology |
| Keyword:
|
connectedness |
| Keyword:
|
completely Hausdorff space |
| Keyword:
|
Urysohn space |
| Keyword:
|
Brown space |
| MSC:
|
54B10 |
| MSC:
|
54D05 |
| MSC:
|
54D10 |
| idZBL:
|
Zbl 07511575 |
| idMR:
|
MR4405818 |
| DOI:
|
10.14712/1213-7243.2022.001 |
| . |
| Date available:
|
2022-02-21T13:30:13Z |
| Last updated:
|
2024-01-01 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/149371 |
| . |
| Reference:
|
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| . |
