On quasi-continuous and cliquish maps with values in uniform spaces. (English) Zbl 0579.54008

Ewert, Janina

Bull. Pol. Acad. Sci., Math. 32, 81-88 (1984).

Cliquish multivalued maps \(F: X\to Y\) with compact values (X topological, Y uniform) are defined. The author investigates their relation to various kinds of continuity and preservation by limits. The main result: If X is a Baire space and F is the pointwise limit of u-quasicontinuous maps, then F is cliquish provided either each \(F_ n\) is \(\ell\)- quasicontinuous or Y is a second countable space.

Reviewer: M.Hušek

MSC:

54C10	Special maps on topological spaces (open, closed, perfect, etc.)
54C60	Set-valued maps in general topology

Keywords:

Cliquish multivalued maps; continuity; preservation by limits; Baire space