UPPER AND LOWER COMPLETELY CONTINUOUS MULTIFUNCTIONS

J. K. KOHLI(1) and C. P. ARYA(2)

1. Department of Mathematics, Hindu College, University of Delhi, Delhi 110007, INDIA
e-mail: jk_kohli@ yahoo.co.in 2. ISSA/DRDO, Metcalfe House, Delhi 110054, INDIA.
e-mail: carya28@ gmail.com

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.

Keywords

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.
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