Abstract
The notion of complete continuity of functions (Kyungpook Math. J. 14(1974), 131-143) is extended to the realm of multifunctions. Basic properties of upper (lower) completely continuous multifunctions are studied and their place in the hierarchy of variants of con-tinuity of multifunctions is elaborated. Examples are included to reflect upon the distinc-tiveness of upper (lower) complete continuity of multifunctions from that of other vari-ants of continuity of multifunctions which already exist in the literature. Interplay be-tween topological properties and completely continuous multifunctions is considered.
Cuvinte cheie
upper/lower (almost) completely continuous multifunction
upper/lower (almost) cl-supercontinuous multifunction
upper/lower (almost) z-supercontinuous multifunction
upper/lower (almost) perfectly continuous multifunction
S-closed
almost regular
almost completely regular
nearly compact
nearly paracompact.