Long and Herrington  have investigated some properties of the strongly ?-continuous functions. In this paper we strengthen some of these properties of Long and Herrington  by studying a new class of functions, called HC-continuous functions.
Authors:M. E. Abd El-Monsef, I. M. Hanafy, and S. N. El-Deeb
The concept of (ϑ,s)-continuity  is considered and studied in fuzzy setting. It is seen that althought it is independent with each of the concepts of fuzzy continuity , fuzzy σ-continuity , fuzzy almost continuity  and fuzzy semicontinuity ; it implies fuzzy weak continuity , but the converse may not be true. The image of a compact fts  under a fuzzy (ϑ,s)-continuous surjective function isS-closed . Finally the concepts of fuzzy (ϑ,s)-closed graphs, fuzzy (ϑ,s)-T2 spaces and fuzzy Urysohn spaces are introduced and mainly their connections with fuzzy (ϑ,s)-continuity are studied.