On S-Subcontinuous multifunctions

Abstract

R.V. Fuller in [5] introduced the concept of subcontinuous function and
used it to obtain conditions implying continuity. In [9] R. E. Simthson
extended this concept to multifunctions and used it to obtain a number of
results on multifunctions, and also developed criteria under which a
multifunction is upper semi continuous.
In this paper we introduce the notion of s-subcontinuity for
multifunction as a generalization of subcontinuity and use it to obtain
many results on multifunction with s-closed graphs. Conditions implying
upper semi continuity [8] for multifunction are derived.
Several characterizations for upper semi-continuity and lower semi
continuity [8] are obtained using filterbasis.