7 papers
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…
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…
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…
Ordinal Decompositions and Extreme Selections
Valentin Gutev
The paper contains two natural constructions of extreme hyperspace selections generated by special ordinal decompositions of the underlying space. These constructions are very effi…
On real-valued functions of Lipschitz type
Valentin Gutev
The classical McShane-Whitney extension theorem for Lipschitz functions is refined by showing that for a closed subset of the domain, it remains valid for any interval of the real…
Butterfly Points and 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 mi…
Extension of Hyperspace Selections
Valentin Gutev
In 1951, Ernest Michael wrote a definitive seminal article on hyperspaces raising a general question that became known as the hyperspace selection problem. The present paper contai…