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math.FA2026
Kirszbraun's Intersection Property and Nonexpansive Extensions
Valentin Gutev
This paper aims to present the historical development of the extension problem of nonexpansive maps in Euclidean and Hilbert spaces, and to serve as a comprehensive guide to this s…
math.GN2026
On the Variety of Hyperspace Selections
Valentin Gutev
If is a continuous selection for the Vietoris hyperspace of the nonempty closed subsets of a space , then the point is not as arbitrary as it…
math.FA2026
Continuous Selections, Function Spaces and Partitions of Unity
Valentin Gutev
The famous Michael selection theorem deals with the characterisation of paracompact spaces by continuous selections of lower semi-continuous mappings in Banach spaces. In this pape…