Modified Whyburn semigroups.
We consider the question of when , where is the elementary submodel topology on X ∩ M, especially in the case when is compact.
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.