On first countable quasitopological homotopy groups
| Autor: | Hamid Torabi |
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| Rok vydání: | 2021 |
| Předmět: | |
| Zdroj: | Mathematica Slovaca. 71:773-779 |
| ISSN: | 1337-2211 0139-9918 |
| DOI: | 10.1515/ms-2021-0019 |
| Popis: | If q: X → Y is a quotient map, then, in general, q × q: X × X → Y × Y may fail to be a quotient map. In this paper, by reviewing the concept of homotopy groups and quotient maps, we find under which conditions the map q × q is a quotient map, where q: Ω n (X, x 0) → πn (X, x 0), is the natural quotient map from the nth loop space of (X, x 0), Ω n (X, x 0), with compact-open topology to the quasitopological nth homotopy group πn (X, x 0). Ultimately, using these results, we found some properties of first countable homotopy groups. |
| Databáze: | OpenAIRE |
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