| Title:
|
$LJ$-spaces (English) |
| Author:
|
Gao, Yin-Zhu |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
57 |
| Issue:
|
4 |
| Year:
|
2007 |
| Pages:
|
1223-1237 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper $LJ$-spaces are introduced and studied. They are a common generalization of Lindelöf spaces and $J$-spaces researched by E. Michael. A space $X$ is called an $LJ$-space if, whenever $\lbrace A,B\rbrace $ is a closed cover of $X$ with $A\cap B$ compact, then $A$ or $B$ is Lindelöf. Semi-strong $LJ$-spaces and strong $LJ$-spaces are also defined and investigated. It is demonstrated that the three spaces are different and have interesting properties and behaviors. (English) |
| Keyword:
|
$LJ$-spaces |
| Keyword:
|
Lindelöf |
| Keyword:
|
$J$-spaces |
| Keyword:
|
$L$-map |
| Keyword:
|
(countably) compact |
| Keyword:
|
perfect map |
| Keyword:
|
order topology |
| Keyword:
|
connected |
| Keyword:
|
topological linear spaces |
| MSC:
|
54D20 |
| MSC:
|
54D30 |
| MSC:
|
54F05 |
| MSC:
|
54F65 |
| idZBL:
|
Zbl 1174.54012 |
| idMR:
|
MR2357588 |
| . |
| Date available:
|
2009-09-24T11:52:35Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/128235 |
| . |
| Reference:
|
[1] R. R. Engelking: General Topology.Revised and completed edition, Heldermann Verlag, Berlin, 1989. Zbl 0684.54001, MR 1039321 |
| Reference:
|
[2] Y. Kodama and K. Nagami: Theory of General Topology.Iwanami, Tokyo, 1974. (Japanese) |
| Reference:
|
[3] E. Michael: $J$-spaces.Top. Appl. 102 (2000), 315–339. Zbl 0942.54020, MR 1745451 |
| Reference:
|
[4] E. Michael: A note on closed maps and compact sets.Israel Math. J. 2 (1964), 173–176. Zbl 0136.19303, MR 0177396, 10.1007/BF02759940 |
| Reference:
|
[5] E. Michael: A survey of $J$-spaces.Proceeding of the Ninth Prague Topological Symposium Contributed papers from the Symposium held in Prague Czech Republic, August 19–25, 2001, pp. 191–193. MR 1906840 |
| Reference:
|
[6] J. R. Munkres: Topology.Prentice-Hall, Englewood Cliffs, NJ, 1975. Zbl 0306.54001, MR 0464128 |
| Reference:
|
[7] K. Nowinski: Closed mappings and the Freudenthal compactification.Fund. Math. 76 (1972), 71–83. Zbl 0235.54023, MR 0324628, 10.4064/fm-76-1-71-83 |
| Reference:
|
[8] L. A. Steen and J. A. Seebach, Jr: Counterexamples in Topology.Springer-Verlag, New York, 1978. MR 0507446 |
| . |
