Rodrigo Hidalgo Linares, Oleg Okunev
Free locally convex spaces and L-retracts

Comment.Math.Univ.Carolin. 64,1 (2023) 19-37.

Abstract: We study the relation of L-equivalence defined between Tychonoff spaces, that is, we study the topological isomorphisms of their respective free locally convex spaces. We introduce the concept of an L-retract in a Tychonoff space in terms of the existence of a special kind of simultaneous extensions of continuous functions, explore the relation of this concept with the Dugundji extension theorem, and find some conditions that allow us to identify L-retracts in various classes of topological spaces. As applications, we present a method for constructing examples of L-equivalent mappings and L-equivalent spaces and in particular, we show that the properties of being an open mapping or a perfect mapping are not L-invariant.

Keywords: free locally convex space; L-equivalence; retraction

DOI: DOI 10.14712/1213-7243.2023.017
AMS Subject Classification: 46A03