Article
| Title: | A note on functional tightness and minitightness of space of the $G$-permutation degree (English) |
| Author: | Georgiou, Dimitrios N. |
| Author: | Mamadaliev, Nodirbek K. |
| Author: | Zhuraev, Rustam M. |
| Language: | English |
| Journal: | Commentationes Mathematicae Universitatis Carolinae |
| ISSN: | 0010-2628 (print) |
| ISSN: | 1213-7243 (online) |
| Volume: | 64 |
| Issue: | 1 |
| Year: | 2023 |
| Pages: | 97-108 |
| Summary lang: | English |
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| Category: | math |
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| Summary: | We study the behavior of the minimal tightness and functional tightness of topological spaces under the influence of the functor of the permutation degree. Analytically: a) We introduce the notion of $\tau$-open sets and investigate some basic properties of them. b) We prove that if the map $f\colon X\rightarrow Y$ is $\tau$-continuous, then the map $SP^{n}f\colon SP^n X \rightarrow SP^n Y$ is also $\tau$-continuous. c) We show that the functor $SP^n$ preserves the functional tightness and the minimal tightness of compacts. d) Finally, we give some facts and properties on $\tau$-bounded spaces. More precisely, we prove that the functor of permutation degree $SP^n$ preserves the property of being $\tau$-bounded. (English) |
| Keyword: | $\tau$-open set |
| Keyword: | $\tau$-bounded space |
| Keyword: | functional tightness |
| Keyword: | minimal tightness |
| MSC: | 54B20 |
| MSC: | 54C05 |
| idZBL: | Zbl 07790585 |
| idMR: | MR4631793 |
| DOI: | 10.14712/1213-7243.2023.019 |
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| Date available: | 2023-08-28T09:48:46Z |
| Last updated: | 2024-02-13 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/151802 |
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| Reference: | [1] Arhangel'skiĭ A. V.: Functional tightness, $Q$-spaces and $\tau$-embeddings.Comment. Math. Univ. Carolin. 24 (1983), no. 1, 105–120. MR 0703930 |
| Reference: | [2] Beshimov R. B.: Some properties of the functor $O_{\beta}$.Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI) 313 (2004), Issled. po Topol. 11, 131–134, 139 (Russian); translation in J. Math. Sci. (N.Y.) 133 (2006), no. 5, 1599–1601. MR 2091586 |
| Reference: | [3] Beshimov R. B.: Nonincrease of density and weak density under weakly normal functors.Mat. Zametki 84 (2008), no. 4, 527–531 (Russian); translation in Math. Notes 84 (2008), no. 3–4, 493–497. MR 2485193 |
| Reference: | [4] Beshimov R. B., Georgiou D. N., Mamadaliev N. K.: On $\tau$-bounded spaces and hyperspaces.Filomat 36 (2022), no. 1, 187–193. MR 4394261, 10.2298/FIL2201187B |
| Reference: | [5] Beshimov R. B., Georgiou D. N., Zhuraev R. M.: Index boundedness and uniform connectedness of space of the $G$-permutation degree.Appl. Gen. Topol. 22 (2021), no. 2, 447–459. MR 4359780, 10.4995/agt.2021.15566 |
| Reference: | [6] Beshimov R. B., Mamadaliev N. K.: On the functor of semiadditive $\tau$-smooth functionals.Topology Appl. 221 (2017), 167–177. MR 3624454, 10.1016/j.topol.2017.02.037 |
| Reference: | [7] Beshimov R. B., Mamadaliev N. K.: Categorical and topological properties of the functor of Radon functionals.Topology Appl. 275 (2020), 106998, 11 pages. MR 4081635, 10.1016/j.topol.2019.106998 |
| Reference: | [8] Beshimov R. B., Mamadaliev N. K., Èshtemirova S. K.: Categorical and cardinal properties of hyperspaces with a finite number of components.Itogi Nauki Tekh. Ser. Sovrem. Mat. Priloyh. Temat. Obz. 144 (2018), 96–103 (Russian); translation in J. Math. Sci. 245 (2020), no. 3, 390–397. MR 3829876 |
| Reference: | [9] Fedorčuk V. V.: Covariant functors in a category of compacta, absolute retracts and $Q$-manifolds.Uspekhi Mat. Nauk 36 (1981), no. 3(219), 177–195, 256 (Russian). MR 0622724 |
| Reference: | [10] Fedorchuk V. V., Filippov V. V.: Topology of hyperspaces and its applications.Current Life, Science and Technology: Series “Mathematics and Cybernetics" 89 (1989), no. 4, 48 pages (Russian). MR 1000972 |
| Reference: | [11] Fedorchuk V. V., Filippov V. V.: General Topology.The Basic Foundation, Fizmatlit, Moscow, 2006. |
| Reference: | [12] Maya D., Pellicer-Covarrubias P., Pichardo-Mendoza R.: Cardinal functions of the hyperspace of convergent sequences.Math. Slovaca 68 (2018), no. 2, 431–450. MR 3783397, 10.1515/ms-2017-0114 |
| Reference: | [13] Michael E.: Topologies on spaces of subsets.Trans. Amer. Math. Soc. 71 (1951), 152–172. Zbl 0043.37902, MR 0042109, 10.1090/S0002-9947-1951-0042109-4 |
| Reference: | [14] Okunev O.: The minitightness of products.Topology Appl. 208 (2016), 10–16. MR 3506966, 10.1016/j.topol.2016.05.003 |
| Reference: | [15] Okunev O., Ramírez Páramo R.: Functional tightness, $R$-quotient mappings and products.Topology Appl. 228 (2017), 236–242. MR 3679085, 10.1016/j.topol.2017.06.009 |
| Reference: | [16] Radul T.: On the functor of order-preserving functionals.Comment. Math. Univ. Carol. 39 (1998), no. 3, 609–615. Zbl 0962.54009, MR 1666806 |
| Reference: | [17] Reznichenko E. A.: Functional and weak functional tightness.Topological Structures and Their Maps, Latv. Gos. Univ., Riga, 1987, pages 105–107. MR 0934036 |
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