Characterization of Semi-continuity in the Product Space

Abstract

In this short note we revisit the concepts of semi-open set and semi-continuity and give some properties of semi-open sets in the Cartesian product with the Tychonoff topology. Further, characterize semi-continuous functions from a topological space into the product space. The result we obtain runs parallel to the one we have for continuous functions in the product space. Other results involving semi-continuous functions in the product space will also be given.