A Note on Normal Generalized Topological Spaces

In this paper, we show by means of examples that the Urysohn's lemma is not necessarily valid for a normal generalized topological space. Using a GT-analog of the Urysohn's lemma, we show that the following two statements are equivalent for a Hausdorff normal generalized topological space X with the property that each closed set is a Gδ-set:(i) X is a topological space.(ii) The set of nonnegative lower semi-continuous functions on X is closed under the operations of addition and multiplication.

کلیدواژه ها:

Normal generalized topological space ، lower semi-continuous function ، Urysohn's lemma