| Title:
|
Normal spaces and the Lusin-Menchoff property (English) |
| Author:
|
Pyrih, Pavel |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
122 |
| Issue:
|
3 |
| Year:
|
1997 |
| Pages:
|
295-299 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We study the relation between the Lusin-Menchoff property and the $F_\sigma$-"semiseparation" property of a fine topology in normal spaces. Three examples of normal topological spaces having the $F_\sigma$-"semiseparation" property without the Lusin-Menchoff property are given. A positive result is obtained in the countable compact space. (English) |
| Keyword:
|
fine topology |
| Keyword:
|
finely separated sets |
| Keyword:
|
Lusin-Menchoff property |
| Keyword:
|
normal space |
| MSC:
|
26A03 |
| MSC:
|
31C40 |
| MSC:
|
54A10 |
| idZBL:
|
Zbl 0897.54001 |
| idMR:
|
MR1600656 |
| DOI:
|
10.21136/MB.1997.126145 |
| . |
| Date available:
|
2009-09-24T21:26:38Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/126145 |
| . |
| Reference:
|
[1] Laczkovich M.: Separation properties of some subclasses of Baire 1 functions.Acta Math. Acad. Sci. Hungar. 26 (1975), 405-421. Zbl 0316.54014, MR 0404543, 10.1007/BF01902349 |
| Reference:
|
[2] Lukeš J., Malý J., Zajíček L.: Fine Topology Methods in Real Analysis and Potential Theory.Lecture Notes in Mathematics 1189, Springer-Verlag, Berlin, 1986. MR 0861411 |
| Reference:
|
[3] Lukeš J., Zajíček L.: The insertion of $G_{\delta}$ sets and fine topologies.Comment. Math. Univ. Carolin. 18 (1977), 101-104. Zbl 0355.26003, MR 0447497 |
| Reference:
|
[4] Malý J.: A note on separation of sets by approximately continuous functions.Comment. Math. Univ. Carolin. 20 (1979), 579-588. Zbl 0406.26004, MR 0539552 |
| Reference:
|
[5] Pyrih P.: Separation of finely closed sets by finely open sets.Real Anal. Exchange 21 (1995/96), no. 1, 345-348. MR 1377547 |
| Reference:
|
[6] Tall F.D.: Normal subspaces of the density topology.Pacific J. Math. 75 (1978), 579-588. Zbl 0345.54015, MR 0500830, 10.2140/pjm.1978.75.579 |
| . |
