Super-Open Sets and Super-Continuity of Maps in the Product Space

Abstract

In this short note we took another look at the concepts of super-open and super-closed sets and super-continuity and gave some properties of these concepts in the Cartesian product with the Tychonoff topology. Further, we characterized super-continuous functions from an arbitrary topological space into the product space. The result we obtained runs parallel to the one we have for continuous functions in the product space. Other results involving super-continuous functions in the product space are also given. Keywords: super-open; super-closed; super-closure; super-interior; super-continuous. 2010 Mathematics Subject Classification: 54C05