International Journal of Mathematics and Mathematical Sciences
Volume 7 (1984), Issue 4, Pages 809-816
doi:10.1155/S0161171284000831

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.