Some Remarks on Closure and Strong Continuity

Abstract

Noire studied several properties of weak continuity in Proc. Amer. Math. Soc. 46(1), 120-124. In this paper it is shown that similar to most of the results of the above paper still hold for closure and strong continuity. Example 2 is a counterexample to a corollary to Theorem 6 of Long and Herrington. Theorem 12 of our paper is a sharper result to Theorem 5 of Noire. Several decomposition theorems of closure and strong continuity are obtained.