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Free locally convex spaces and L -retracts

Rodrigo Hidalgo Linares, Oleg Okunev (2023)

Commentationes Mathematicae Universitatis Carolinae

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....

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