On generalization of homotopy axiom
In [S. Kermit, Proc. Amer. Math. Soc., 1972, 31(1):271-275] it was proven that if G is compact topological group or field then in the homotopy axiom for Alexander-Spanier-Kolmogoroff cohomology the parameter segment [0;1] can be replaced by any compact connected space T. The purpose of the paper is...
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| Format: | Article |
| Language: | English |
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Odesa National University of Technology
2023-11-01
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| Series: | Pracì Mìžnarodnogo Geometričnogo Centru |
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| Online Access: | https://journals.ontu.edu.ua/index.php/geometry/article/view/2536 |
| _version_ | 1797629880704172032 |
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| author | Umed Karimov |
| author_facet | Umed Karimov |
| author_sort | Umed Karimov |
| collection | DOAJ |
| description | In [S. Kermit, Proc. Amer. Math. Soc., 1972, 31(1):271-275] it was proven that if G is compact topological group or field then in the homotopy axiom for Alexander-Spanier-Kolmogoroff cohomology the parameter segment [0;1] can be replaced by any compact connected space T. The purpose of the paper is to show that the parameter space T can not be replaced in general by locally compact connected space. |
| first_indexed | 2024-03-11T10:59:01Z |
| format | Article |
| id | doaj.art-3f1db7747ed849209ea1a6a577a503a3 |
| institution | Directory Open Access Journal |
| issn | 2072-9812 2409-8906 |
| language | English |
| last_indexed | 2024-03-11T10:59:01Z |
| publishDate | 2023-11-01 |
| publisher | Odesa National University of Technology |
| record_format | Article |
| series | Pracì Mìžnarodnogo Geometričnogo Centru |
| spelling | doaj.art-3f1db7747ed849209ea1a6a577a503a32023-11-12T13:56:15ZengOdesa National University of TechnologyPracì Mìžnarodnogo Geometričnogo Centru2072-98122409-89062023-11-0116318319110.15673/pigc.v16i3.25362536On generalization of homotopy axiomUmed Karimov0Institute of Mathematics, Academy of Sciences of TajikistanIn [S. Kermit, Proc. Amer. Math. Soc., 1972, 31(1):271-275] it was proven that if G is compact topological group or field then in the homotopy axiom for Alexander-Spanier-Kolmogoroff cohomology the parameter segment [0;1] can be replaced by any compact connected space T. The purpose of the paper is to show that the parameter space T can not be replaced in general by locally compact connected space.https://journals.ontu.edu.ua/index.php/geometry/article/view/2536alexander-spanier-kolmogoroff cohomologycech cohomologyhomotopy axiommilnor-kharlap exact sequence |
| spellingShingle | Umed Karimov On generalization of homotopy axiom Pracì Mìžnarodnogo Geometričnogo Centru alexander-spanier-kolmogoroff cohomology cech cohomology homotopy axiom milnor-kharlap exact sequence |
| title | On generalization of homotopy axiom |
| title_full | On generalization of homotopy axiom |
| title_fullStr | On generalization of homotopy axiom |
| title_full_unstemmed | On generalization of homotopy axiom |
| title_short | On generalization of homotopy axiom |
| title_sort | on generalization of homotopy axiom |
| topic | alexander-spanier-kolmogoroff cohomology cech cohomology homotopy axiom milnor-kharlap exact sequence |
| url | https://journals.ontu.edu.ua/index.php/geometry/article/view/2536 |
| work_keys_str_mv | AT umedkarimov ongeneralizationofhomotopyaxiom |