Article
| Title: | Free locally convex spaces and $L$-retracts (English) |
| Author: | Hidalgo Linares, Rodrigo |
| Author: | Okunev, Oleg |
| Language: | English |
| Journal: | Commentationes Mathematicae Universitatis Carolinae |
| ISSN: | 0010-2628 (print) |
| ISSN: | 1213-7243 (online) |
| Volume: | 64 |
| Issue: | 1 |
| Year: | 2023 |
| Pages: | 19-37 |
| Summary lang: | English |
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| Category: | math |
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| Summary: | 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. (English) |
| Keyword: | free locally convex space |
| Keyword: | $L$-equivalence |
| Keyword: | retraction |
| MSC: | 46A03 |
| idZBL: | Zbl 07790580 |
| idMR: | MR4631788 |
| DOI: | 10.14712/1213-7243.2023.017 |
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| Date available: | 2023-08-28T09:38:48Z |
| Last updated: | 2024-02-13 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/151806 |
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