| Title:
|
On relatively almost Lindelöf subsets (English) |
| Author:
|
Song, Yankui |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
134 |
| Issue:
|
2 |
| Year:
|
2009 |
| Pages:
|
183-190 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
A subspace $Y$ of a space $X$ is almost Lindelöf (strongly almost Lindelöf) in $X$ if for every open cover $\mathcal U$ of $X$ (of $Y$ by open subsets of $X$), there exists a countable subset $\mathcal V$ of $\mathcal U$ such that $Y\subseteq \bigcup \{\overline V\: V\in \mathcal V\}$. In this paper we investigate the relationships between relatively almost Lindelöf subset and relatively strongly almost Lindelöf subset by giving some examples, and also study various properties of relatively almost Lindelöf subsets and relatively strongly almost Lindelöf subsets. (English) |
| Keyword:
|
Lindelöf space |
| Keyword:
|
strongly Lindelöf subset |
| Keyword:
|
almost Lindelöf subset |
| Keyword:
|
strongly almost Lindelöf subset |
| MSC:
|
54D15 |
| MSC:
|
54D20 |
| idZBL:
|
Zbl 1212.54079 |
| idMR:
|
MR2535146 |
| DOI:
|
10.21136/MB.2009.140653 |
| . |
| Date available:
|
2010-07-20T17:57:13Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140653 |
| . |
| Reference:
|
[1] Arhangel'skii, A. V., Hamdi, M. M., Genedi: The beginnings of the theory of relative topological properties.General Topology. Spaces and Functions, MGU, Moskva (1989), 3-48 Russian. |
| Reference:
|
[2] Arhangel'skii, A. V.: A generic theorem in the theory of cardinal invariants of topological spaces.Comment. Math. Univ. Carolinae 36 (1995), 303-325. MR 1357532 |
| Reference:
|
[3] Engelking, R.: General Topology.Revised and completed edition, Heldermann (1989). Zbl 0684.54001, MR 1039321 |
| Reference:
|
[4] Kočinac, Lj. D.: Some relative topological properties.Mat. Vesn. 44 (1992), 33-44. MR 1201265 |
| Reference:
|
[5] Cammaroto, F., Santoro, G.: Some counterexamples and properties on generalizations of Lindelöf spaces.Int. J. Math. Math. Sci. 19 (1996), 737-746. Zbl 0860.54033, MR 1397840, 10.1155/S0161171296001020 |
| Reference:
|
[6] Willard, S., Dissanayake, U. N. B.: The almost Lindelöf degree.Can. Math. Bull. 27 (1984), 452-455. Zbl 0551.54003, MR 0763044, 10.4153/CMB-1984-070-2 |
| . |
