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Some classes of topological spaces and the space of G-permutation degree

  • Ljubiša D. R. Kočinac EMAIL logo , Farkhod G. Mukhamadiev and Anvar K. Sadullaev
Published/Copyright: October 14, 2023
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Abstract

In this paper, we study the behavior of some classes of topological spaces under the influence of the functor of G-permutation degree 𝖲𝖯 G n . We prove:

  1. if a space X is an r-space, then so is 𝖲𝖯 G n X ,

  2. if X is a cosmic space, then so is 𝖲𝖯 G n X ,

  3. if a space X is a C ( κ ) -cosmic, then so is 𝖲𝖯 G n X ,

  4. if a space X is an α-space, then so is 𝖲𝖯 G n X .

Keywords: cosmic space
MSC 2020: 18F60; 54B30; 54E99

Acknowledgements

We thank the referee for some suggestions which helped us to improve the manuscript.

References

[1] R. B. Beshimov, Some properties of the functor O β , Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI) 313 (2004), no. 11, 131–134; translation in J. Math. Sci. (N. Y.) 133 (2006), no. 5, 1599–1601. Search in Google Scholar

[2] R. B. Beshimov, D. N. Georgiou and N. K. Mamadaliev, On τ-bounded spaces and hyperspaces, Filomat 36 (2022), no. 1, 187–193. 10.2298/FIL2201187BSearch in Google Scholar

[3] R. B. Beshimov, D. N. Georgiou, F. Sereti and R. M. Zhuraev, Metric, stratifiable and uniform spaces of G-permutation degree, Math. Slovaca, to appear. Search in Google Scholar

[4] R. B. Beshimov, D. N. Georgiou and R. M. Zhuraev, Index boundedness and uniform connectedness of space of the G-permutation degree, Appl. Gen. Topol. 22 (2021), no. 2, 447–459. 10.4995/agt.2021.15566Search in Google Scholar

[5] R. B. Beshimov and D. T. Safarova, Some topological properties of a functor of finite degree, Lobachevskii J. Math. 42 (2021), no. 12, 2744–2753. 10.1134/S1995080221120088Search in Google Scholar

[6] R. Engelking, General Topology, 2nd ed., Sigma Ser. Pure Math. 6, Heldermann, Berlin, 1989. Search in Google Scholar

[7] V. V. Fedorčuk, Covariant functors in a category of compacta, absolute retracts and Q-manifolds, Uspekhi Mat. Nauk 36 (1981), no. 3(219), 177–195. 10.1070/RM1981v036n03ABEH004251Search in Google Scholar

[8] V. V. Fedorchuk and V. V. Filippov, General Topology. The Basic Constructions (in Russian), Izd-vo MGU, Moscow, 1988. Search in Google Scholar

[9] V. V. Fedorchuk and V. V. Filippov, Topology of Hyperspaces and Its Applications, Current Life Sci. Technol. Ser. Math. Cybernetics 89, “Znanie”, Moscow, 1989. Search in Google Scholar

[10] D. N. Georgiou, S. D. Iliadis and A. C. Megaritis, C ( τ ) -cosmic spaces, Topology Proc. 38 (2011), 149–164. Search in Google Scholar

[11] C. Good and S. Macías, Symmetric products of generalized metric spaces, Topology Appl. 206 (2016), 93–114. 10.1016/j.topol.2016.03.019Search in Google Scholar

[12] K. P. Hart, J. Nagata and J. E. Vaughan, Encyclopedia of General Topology, Elsevier Science, Amsterdam, 2004. Search in Google Scholar

[13] L. D. R. Kočinac and F. G. Mukhamadiev, Some properties of the N τ φ -nucleus, Topology Appl. 326 (2023), Paper No. 108430. 10.1016/j.topol.2023.108430Search in Google Scholar

[14] L. D. R. Kočinac, F. G. Mukhamadiev and A. K. Sadullaev, Some cardinal and geometric properties of the space of permutation degree, Axioms 11 (2022), no. 6, Paper No. 290. 10.3390/axioms11060290Search in Google Scholar

[15] L. D. R. Kočinac, F. G. Mukhamadiev and A. K. Sadullaev, Some topological and cardinal properties of the space of permutation degree, Filomat 36 (2022), no. 20, 7059–7066. 10.2298/FIL2220059KSearch in Google Scholar

[16] L. D. R. Kočinac, F. G. Mukhamadiev and A. K. Sadullaev, Tightness-type properties of the space of permutation degree, Mathematics 10 (2022), no. 18, Paper No. 3341. 10.3390/math10183341Search in Google Scholar

[17] E. Michael, 0 -spaces, J. Math. Mech. 15 (1966), 983–1002. 10.1512/iumj.1966.15.15066Search in Google Scholar

[18] F. G. Mukhamadiev, On certain cardinal properties of the N τ φ -nucleus of a space X, J. Math. Sci. 245 (2020), no. 3, 411–415. 10.1007/s10958-020-04704-5Search in Google Scholar

[19] T. K. Yuldashev and F. G. Mukhamadiev, The local density and the local weak density in the space of permutation degree and in Hattori space, Ural Math. J. 6 (2020), no. 2, 108–116. 10.15826/umj.2020.2.011Search in Google Scholar

[20] T. K. Yuldashev and F. G. Mukhamadiev, Caliber of space of subtle complete coupled systems, Lobachevskii J. Math. 42 (2021), no. 12, 3043–3047. 10.1134/S1995080221120398Search in Google Scholar

Received: 2023-04-04
Revised: 2023-04-28
Accepted: 2023-05-10
Published Online: 2023-10-14
Published in Print: 2024-04-01

© 2023 Walter de Gruyter GmbH, Berlin/Boston

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