Functor of weakly additive τ-smooth functionals and mappings
We present a criterion for the τ-smoothness of weakly additive order-preserving functionals and establish that the functor of τ-smooth weakly additive functionals preserves the perfectness of mappings. We prove that if a continuous mapping between Tikhonov spaces is such that the mapping between the...
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| Date: | 2009 |
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| Main Authors: | , , , |
| Format: | Article |
| Language: | English |
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Institute of Mathematics, NAS of Ukraine
2009
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/3089 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860509109274542080 |
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| author | Ayupov, Sh. A. Zaitov, A. A. Аюпов, Ш. A. Заитов, A. A. Аюпов, Ш. A. Заитов, A. A. |
| author_facet | Ayupov, Sh. A. Zaitov, A. A. Аюпов, Ш. A. Заитов, A. A. Аюпов, Ш. A. Заитов, A. A. |
| author_sort | Ayupov, Sh. A. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-18T19:45:12Z |
| description | We present a criterion for the τ-smoothness of weakly additive order-preserving functionals and establish that the functor of τ-smooth weakly additive functionals preserves the perfectness of mappings. We prove that if a continuous mapping between Tikhonov spaces is such that the mapping between the corresponding spaces of weakly additive functionals generated by it is open, then the indicated mapping is also open. It is shown that the converse statement is true under certain additional conditions. |
| first_indexed | 2026-03-24T02:35:52Z |
| format | Article |
| fulltext | |
| id | umjimathkievua-article-3089 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2026-03-24T02:35:52Z |
| publishDate | 2009 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | |
| spelling | umjimathkievua-article-30892020-03-18T19:45:12Z Functor of weakly additive τ-smooth functionals and mappings Functor of weakly additive τ-smooth functionals and mappings Ayupov, Sh. A. Zaitov, A. A. Аюпов, Ш. A. Заитов, A. A. Аюпов, Ш. A. Заитов, A. A. We present a criterion for the τ-smoothness of weakly additive order-preserving functionals and establish that the functor of τ-smooth weakly additive functionals preserves the perfectness of mappings. We prove that if a continuous mapping between Tikhonov spaces is such that the mapping between the corresponding spaces of weakly additive functionals generated by it is open, then the indicated mapping is also open. It is shown that the converse statement is true under certain additional conditions. Наведено критерій τ-гладкості слабкоадитивних зберігаючих порядок функціоналів i встановлено, що функтор τ-гладких слабкоадитивних функціоналів зберігає досконалість відображень. Доведено, що якщо неперервне відображення між тихоновськими просторами таке, що породжене ним відображення між відповідними просторами слабкоадитивних функціоналів є відкритим, то задане відображення також є відкритим. Справедливість оберненого твердження показано при додаткових умовах. Institute of Mathematics, NAS of Ukraine 2009-09-25 Article Article https://umj.imath.kiev.ua/index.php/umj/article/view/3089 Ukrains’kyi Matematychnyi Zhurnal; Vol. 61 No. 9 (2009); 1167-1173 Український математичний журнал; Том 61 № 9 (2009); 1167-1173 1027-3190 en https://umj.imath.kiev.ua/index.php/umj/article/view/3089/2927 Copyright (c) 2009 Ayupov Sh. A.; Zaitov A. A. |
| spellingShingle | Ayupov, Sh. A. Zaitov, A. A. Аюпов, Ш. A. Заитов, A. A. Аюпов, Ш. A. Заитов, A. A. Functor of weakly additive τ-smooth functionals and mappings |
| title | Functor of weakly additive τ-smooth functionals and mappings |
| title_alt | Functor of weakly additive τ-smooth functionals and mappings |
| title_full | Functor of weakly additive τ-smooth functionals and mappings |
| title_fullStr | Functor of weakly additive τ-smooth functionals and mappings |
| title_full_unstemmed | Functor of weakly additive τ-smooth functionals and mappings |
| title_short | Functor of weakly additive τ-smooth functionals and mappings |
| title_sort | functor of weakly additive τ-smooth functionals and mappings |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/3089 |
| work_keys_str_mv | AT ayupovsha functorofweaklyadditivetsmoothfunctionalsandmappings AT zaitovaa functorofweaklyadditivetsmoothfunctionalsandmappings AT aûpovša functorofweaklyadditivetsmoothfunctionalsandmappings AT zaitovaa functorofweaklyadditivetsmoothfunctionalsandmappings AT aûpovša functorofweaklyadditivetsmoothfunctionalsandmappings AT zaitovaa functorofweaklyadditivetsmoothfunctionalsandmappings |