Jacek Jachymski
Jacek Jachymski: Between Cantor and Smulian: the intersection theorem and its applications
08/12/22 09:57
Tuesday, December 13, 2022 17:00
Location: room C11-3.11
Speaker: Jacek Jachymski (Łódź University of Technology)
Title: Between Cantor and Smulian: the intersection theorem and its applications
Abstract: I will present an intersection theorem for a descending sequence of closed sets for which a convexity type condition is satisfied. However, the condition applies to the whole sequence, not separately to individual sets. I will show that the following theorems follows easily from this result: Smulian's theorem about characterization of reflexive spaces, theorem about the convex set in Hilbert space, and Browder-Gohde-Kirk's theorem about fixed points of nonexpansive mappings.
Location: room C11-3.11
Speaker: Jacek Jachymski (Łódź University of Technology)
Title: Between Cantor and Smulian: the intersection theorem and its applications
Abstract: I will present an intersection theorem for a descending sequence of closed sets for which a convexity type condition is satisfied. However, the condition applies to the whole sequence, not separately to individual sets. I will show that the following theorems follows easily from this result: Smulian's theorem about characterization of reflexive spaces, theorem about the convex set in Hilbert space, and Browder-Gohde-Kirk's theorem about fixed points of nonexpansive mappings.