Weak continuity and strongly closed sets

Abstract

After demonstrating the usual product theorems for weakly continuous functions, strongly closed and extremely closed subsets are contrasted to support the conjecture that a product of faintly continuous functions need not be faintly continuous. Strongly closed sets are used to characterize Hausdorff spaces and Urysohn spaces, and with these characterizations two results obtained by T. Noiri are obtained by function-theoretic means rather than by point-set method.

Keywords

• weak continuity
• faint continuity
• subweak continuity
• strongly closed sets.