Pavel Pyrih, Department of Mathematical Analysis, Charles University, Sokolovska 83, 186 00 Prague 8, Czech Republic, e-mail: pyrih@karlin.mff.cuni.cz
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 (MSC 1991): 54A10, 26A03, 31C40
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