Functional approach to the normality of mappings
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866909222313132032 |
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| author | Liseev, Mikhail Yourievich |
| author_facet | Liseev, Mikhail Yourievich |
| contents | In the article a technique of the usage of $f$-continuous functions (on mappings) and their families is developed. A proof of the Urysohn's Lemma for mappings is presented and a variant of the Brouwer-Tietze-Urysohn Extension Theorem for mappings is proven. Characterizations of the normality properties of mappings are given and the notion of a perfect normality of a mapping is introduced. It seems to be the most optimal in this approach. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_08061 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Functional approach to the normality of mappings Liseev, Mikhail Yourievich General Topology Functional Analysis 55R70, 54C05, 54C08, 54C10, 54D10, 54C20, 54C25, 54D15, 54D35, 54D80 In the article a technique of the usage of $f$-continuous functions (on mappings) and their families is developed. A proof of the Urysohn's Lemma for mappings is presented and a variant of the Brouwer-Tietze-Urysohn Extension Theorem for mappings is proven. Characterizations of the normality properties of mappings are given and the notion of a perfect normality of a mapping is introduced. It seems to be the most optimal in this approach. |
| title | Functional approach to the normality of mappings |
| topic | General Topology Functional Analysis 55R70, 54C05, 54C08, 54C10, 54D10, 54C20, 54C25, 54D15, 54D35, 54D80 |
| url | https://arxiv.org/abs/2406.08061 |