Tightness-Type Properties of the Space of Permutation Degree
In this paper we, prove that if the product <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>X</mi><mi>n</mi></msup></semantics></math></inline-formula> o...
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MDPI AG
2022-09-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/18/3341 |
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| author | Ljubiša D. R. Kočinac Farkhod G. Mukhamadiev Anvar K. Sadullaev |
| author_facet | Ljubiša D. R. Kočinac Farkhod G. Mukhamadiev Anvar K. Sadullaev |
| author_sort | Ljubiša D. R. Kočinac |
| collection | DOAJ |
| description | In this paper we, prove that if the product <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>X</mi><mi>n</mi></msup></semantics></math></inline-formula> of a space <i>X</i> has certain tightness-type properties, then the space of permutation degree <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mi mathvariant="sans-serif">SP</mi><mi mathvariant="sans-serif">n</mi></msup><mi>X</mi></mrow></semantics></math></inline-formula> has these properties as well. It is proven that the set tightness (<i>T</i>-tightness) of the space of permutation degree <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mi mathvariant="sans-serif">SP</mi><mi mathvariant="sans-serif">n</mi></msup><mi>X</mi></mrow></semantics></math></inline-formula> is equal to the set tightness (<i>T</i>-tightness) of the product <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>X</mi><mi>n</mi></msup></semantics></math></inline-formula>. |
| first_indexed | 2024-03-09T23:15:25Z |
| format | Article |
| id | doaj.art-3be034f45c4147839da41cb45f75c288 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T23:15:25Z |
| publishDate | 2022-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-3be034f45c4147839da41cb45f75c2882023-11-23T17:37:02ZengMDPI AGMathematics2227-73902022-09-011018334110.3390/math10183341Tightness-Type Properties of the Space of Permutation DegreeLjubiša D. R. Kočinac0Farkhod G. Mukhamadiev1Anvar K. Sadullaev2Faculty of Sciences and Mathematics, University of Niš, 18000 Niš, SerbiaFaculty of Mathematics, National University of Uzbekistan, Tashkent 100174, UzbekistanDepartment of Exact Sciences, Yeoju Technical Institute in Tashkent, Tashkent 100121, UzbekistanIn this paper we, prove that if the product <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>X</mi><mi>n</mi></msup></semantics></math></inline-formula> of a space <i>X</i> has certain tightness-type properties, then the space of permutation degree <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mi mathvariant="sans-serif">SP</mi><mi mathvariant="sans-serif">n</mi></msup><mi>X</mi></mrow></semantics></math></inline-formula> has these properties as well. It is proven that the set tightness (<i>T</i>-tightness) of the space of permutation degree <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mi mathvariant="sans-serif">SP</mi><mi mathvariant="sans-serif">n</mi></msup><mi>X</mi></mrow></semantics></math></inline-formula> is equal to the set tightness (<i>T</i>-tightness) of the product <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>X</mi><mi>n</mi></msup></semantics></math></inline-formula>.https://www.mdpi.com/2227-7390/10/18/3341functor of permutation degreetightnessset tightness<i>T</i>-tightnessfunctional tightnessmini-tightness |
| spellingShingle | Ljubiša D. R. Kočinac Farkhod G. Mukhamadiev Anvar K. Sadullaev Tightness-Type Properties of the Space of Permutation Degree Mathematics functor of permutation degree tightness set tightness <i>T</i>-tightness functional tightness mini-tightness |
| title | Tightness-Type Properties of the Space of Permutation Degree |
| title_full | Tightness-Type Properties of the Space of Permutation Degree |
| title_fullStr | Tightness-Type Properties of the Space of Permutation Degree |
| title_full_unstemmed | Tightness-Type Properties of the Space of Permutation Degree |
| title_short | Tightness-Type Properties of the Space of Permutation Degree |
| title_sort | tightness type properties of the space of permutation degree |
| topic | functor of permutation degree tightness set tightness <i>T</i>-tightness functional tightness mini-tightness |
| url | https://www.mdpi.com/2227-7390/10/18/3341 |
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