Article
Full entry |
PDF
(0.3 MB)
Feedback
PDF
(0.3 MB)
Feedback
Keywords:
fine topology; finely separated sets; Lusin-Menchoff property; normal space
fine topology; finely separated sets; Lusin-Menchoff property; normal space
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.
References:
[1] Laczkovich M.: Separation properties of some subclasses of Baire 1 functions. Acta Math. Acad. Sci. Hungar. 26 (1975), 405-421. DOI 10.1007/BF01902349 | MR 0404543 | Zbl 0316.54014
[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
[3] Lukeš J., Zajíček L.: The insertion of $G_{\delta}$ sets and fine topologies. Comment. Math. Univ. Carolin. 18 (1977), 101-104. MR 0447497 | Zbl 0355.26003
[4] Malý J.: A note on separation of sets by approximately continuous functions. Comment. Math. Univ. Carolin. 20 (1979), 579-588. MR 0539552 | Zbl 0406.26004
[5] Pyrih P.: Separation of finely closed sets by finely open sets. Real Anal. Exchange 21 (1995/96), no. 1, 345-348. MR 1377547
[6] Tall F.D.: Normal subspaces of the density topology. Pacific J. Math. 75 (1978), 579-588. DOI 10.2140/pjm.1978.75.579 | MR 0500830 | Zbl 0345.54015
Search
Partner of
