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Upper and lower almost cl-supercontinuous multifunctions

Kohli J. K., Arya C. P.

Demonstratio Mathematica

2011

Vol. 44, nr 2

407--421

The notion of almost cl-supercontinuity (≡ almost clopen continuity) of functions (Acta Math. Hungar. 107 (2005), 193–206; Applied Gen. Topology 10 (1) (2009), 1–12) is extended to the realm of multifunctions. Basic properties of upper (lower) almost cl-supercontinuous multifunctions are studied and their place in the hierarchy of strong variants of continuity of multifunctions is discussed. Examples are included to reflect upon the distinctiveness of upper (lower) almost cl-supercontinuity of multifunctions from that of other strong variants of continuity of multifunctions which already exist in the literature.

Attractors of multifunetions

Lasota A., Myjak J.

Bulletin of the Polish Academy of Sciences. Mathematics

2000

Vol. 48, no 3

319-334

We introduce the notion of a semiattractor and attractor for multifunctions and we show that they have properties similar to semifractals and fractals. Further we show a relationship between the multifunctions and transition functions appearing in the theory of Markov operators.

Set-valued iterative square roots of bijections

Powierża T.

Bulletin of the Polish Academy of Sciences. Mathematics

1999

Vol. 47, no 4

377-383

There are different ideas how to generalize the notion of an iterative root, especially when a function does not have a "real" root. We consider a multifunction as a substitute for this notion.