MATHEMATICA BOHEMICA, Vol. 122, No. 3, pp. 295-299 (1997)

Normal spaces and the Lusin-Menchoff property

Pavel Pyrih

Pavel Pyrih, Department of Mathematical Analysis, Charles University, Sokolovska 83, 186 00 Prague 8, Czech Republic, e-mail:

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.

Keywords: fine topology, finely separated sets, Lusin-Menchoff property, normal space

Classification (MSC2000): 54A10, 26A03, 31C40

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