Open and image-open multifunctions. (English) Zbl 0719.54025

Maritz, P.

Glas. Mat., III. Ser. 24(44), No. 2-3, 361-380 (1989).

The author investigates thoroughly properties of openness of multifunctions, especially image-open multifunctions (a multifunction \(F:X\to Y\) is image-P if F(x) has property P for every \(x\in X)\). Interesting theorems on costant semi-continuous and quasi-continuous multifunctions and their graphs are established. Several properties on non-mingled multifunctions (a multifunction F is said to be image-non- mingled if \(F(x_ 1)\cap F(x_ 2)\neq \emptyset\) implies \(F(x_ 1)=F(x_ 2))\) are proved. Theorems of Ponomarev, Stanojević, Munich, Száz, Ceder and Levi are improved. Also a large number of counterexamples is provided.

Reviewer: G.Di Maio (Napoli)

MSC:

54C60	Set-valued maps in general topology
54C10	Special maps on topological spaces (open, closed, perfect, etc.)
54C08	Weak and generalized continuity
54C65	Selections in general topology

Keywords:

image-non-mingled multifunctions; quasi-continuous multifunctions