Normal spaces and the Lusin-Menchoff property

Pavel Pyrih

Mathematica Bohemica (1997)

  • Volume: 122, Issue: 3, page 295-299
  • ISSN: 0862-7959

Abstract

top
We study the relation between the Lusin-Menchoff property and the -“semiseparation” property of a fine topology in normal spaces. Three examples of normal topological spaces having the -“semiseparation” property without the Lusin-Menchoff property are given. A positive result is obtained in the countable compact space.

How to cite

top

Pyrih, Pavel. "Normal spaces and the Lusin-Menchoff property." Mathematica Bohemica 122.3 (1997): 295-299. <http://eudml.org/doc/248129>.

@article{Pyrih1997,
abstract = {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.},
author = {Pyrih, Pavel},
journal = {Mathematica Bohemica},
keywords = {fine topology; finely separated sets; Lusin-Menchoff property; normal space; fine topology; finely separated sets; Lusin-Menchoff property; normal space},
language = {eng},
number = {3},
pages = {295-299},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Normal spaces and the Lusin-Menchoff property},
url = {http://eudml.org/doc/248129},
volume = {122},
year = {1997},
}

TY - JOUR
AU - Pyrih, Pavel
TI - Normal spaces and the Lusin-Menchoff property
JO - Mathematica Bohemica
PY - 1997
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 122
IS - 3
SP - 295
EP - 299
AB - 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.
LA - eng
KW - fine topology; finely separated sets; Lusin-Menchoff property; normal space; fine topology; finely separated sets; Lusin-Menchoff property; normal space
UR - http://eudml.org/doc/248129
ER -

References

top
  1. Laczkovich M., 10.1007/BF01902349, Acta Math. Acad. Sci. Hungar. 26 (1975), 405-421. (1975) Zbl0316.54014MR0404543DOI10.1007/BF01902349
  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. (1986) MR0861411
  3. Lukeš J., Zajíček L., The insertion of sets and fine topologies, Comment. Math. Univ. Carolin. 18 (1977), 101-104. (1977) Zbl0355.26003MR0447497
  4. Malý J., A note on separation of sets by approximately continuous functions, Comment. Math. Univ. Carolin. 20 (1979), 579-588. (1979) Zbl0406.26004MR0539552
  5. Pyrih P., Separation of finely closed sets by finely open sets, Real Anal. Exchange 21 (1995/96), no. 1, 345-348. (1995) MR1377547
  6. Tall F.D., 10.2140/pjm.1978.75.579, Pacific J. Math. 75 (1978), 579-588. (1978) Zbl0345.54015MR0500830DOI10.2140/pjm.1978.75.579

NotesEmbed ?

top

You must be logged in to post comments.