Free locally convex spaces and L -retracts

Rodrigo Hidalgo Linares; Oleg Okunev

Commentationes Mathematicae Universitatis Carolinae (2023)

  • Volume: 64, Issue: 1, page 19-37
  • ISSN: 0010-2628

Abstract

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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.

How to cite

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Hidalgo Linares, Rodrigo, and Okunev, Oleg. "Free locally convex spaces and $L$-retracts." Commentationes Mathematicae Universitatis Carolinae 64.1 (2023): 19-37. <http://eudml.org/doc/299598>.

@article{HidalgoLinares2023,
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.},
author = {Hidalgo Linares, Rodrigo, Okunev, Oleg},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {free locally convex space; $L$-equivalence; retraction},
language = {eng},
number = {1},
pages = {19-37},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Free locally convex spaces and $L$-retracts},
url = {http://eudml.org/doc/299598},
volume = {64},
year = {2023},
}

TY - JOUR
AU - Hidalgo Linares, Rodrigo
AU - Okunev, Oleg
TI - Free locally convex spaces and $L$-retracts
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2023
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 64
IS - 1
SP - 19
EP - 37
AB - 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.
LA - eng
KW - free locally convex space; $L$-equivalence; retraction
UR - http://eudml.org/doc/299598
ER -

References

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