Document Type
Lecture
Publication Date
10-27-2004
Abstract
This talk may be considered as an extension of Brian Davis' talk on topological games on filters. I will go back to a very old theorem of Vainstein (1946), in which he shows that if �� is a closed mapping from a metric space �� onto a metric space ��, then for each �� in ��, the fiber ���� (i.e., the inverse image of �� by the map ��) has a compact boundary. The inverse �� of �� motivates the introduction of upper semicontinuous set-valued maps, and the theorem of Vainstein is actually a predecessor of the Choquet-Dolecki Theorem. Topological games discussed by Brian define one class of spaces in which the Choquet-Dolecki Theorem holds. Another class will be discussed towards the end of my talk.
Relational Format
presentation
Recommended Citation
Labuda, Iwo, "On Structure of Upper Semicontinuity" (2004). Analysis Seminar. 56.
https://egrove.olemiss.edu/math_analysis/56
