Geodesic
Free locally convex spaces and $L$-retracts
Commentationes Mathematicae Universitatis Carolinae, Tome 64 (2023) no. 1, pp. 19-37.

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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.
DOI : 10.14712/1213-7243.2023.017
Classification : 46A03
Keywords: free locally convex space; $L$-equivalence; retraction 
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Hidalgo Linares, Rodrigo; Okunev, Oleg. Free locally convex spaces and $L$-retracts. Commentationes Mathematicae Universitatis Carolinae, Tome 64 (2023) no. 1, pp. 19-37. doi : 10.14712/1213-7243.2023.017. http://geodesic.mathdoc.fr/articles/10.14712/1213-7243.2023.017/

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