Vietoris hyperspaces as quotients of natural function spaces. (English) Zbl 1364.54012

Bartsch, René

Rostocker Math. Kolloq. 69, 55-66 (2014).

It is well known that function space theory has a rich history, providing many results, considering also the topological point of view of function spaces. Thus, it is quite reasonable to study also hyperspaces, equipped with the corresponding topologies, such as the Vietoris topology, and to examine their properties. M. M. Clementino, W. Tholen, G. Beer, A. Lechicki, S. Levi, and S. Naimpally are some of the researchers who studied the Vietoris topology.
In this interesting paper, the author continues to study this topology, in combination with set-open topologies, especially with the compact-open topology. Also, the notion of the Stone-Čech compactification is used to give more characterizations of the Vietoris topology.

Reviewer: Dimitris Georgiou (Patras)

MSC:

54B20	Hyperspaces in general topology
54C35	Function spaces in general topology
54B15	Quotient spaces, decompositions in general topology

Keywords:

hyperspaces; function spaces; quotient spaces; decompositions