SOME PROPERTIES UNIFORM SPACE AND ITS HYPERSPACE

Authors

  • Beshimov Ruzinazar Bebutovich National University of Uzbekistan
  • Safarova Dilnora Teshaboevna National University of Uzbekistan

DOI:

https://doi.org/10.52754/16948645_2023_1_281

Keywords:

Hyperspace, uniformity, uniform space, uniformly connected, uniformly pseudocompact, precompact.

Abstract

In this paper, we will study the connection between a uniformly connected, uniformly pseudocompact, precompact and its hyperspace. It is proved that if a uniform space  is uniformly pseudocompact iff  is uniformly pseudocompact. It is also shown that if a uniform space  is precompact, then a uniform space  is precompact.

References

Beshimov, R.B. Some Topological Properties of a Functor of Finite Degree[Теxt]/ Beshimov R.B., Safarova D.T., // Lobachevskii Journal of Mathematics, 2021, 42(12), стр. 2744–2753. DOI: https://doi.org/10.1134/S1995080221120088

Beshimov, R.B. Index boundedness and uniform connectedness of space of the G-permutation degree[Теxt]/ Beshimov R.B., Georgiou D.N., Zhuraev R.M. // Applied General Topology, 2021, 22(2), стр. 447–459. DOI: https://doi.org/10.4995/agt.2021.15566

Borubaev, A.A. The functor of idempotent probability measures and maps with uniformity properties of uniform spaces[Теxt]/ Borubaev A.A., Eshkobilova D.T. // Eurasian Mathematical Journal, 2021, 12 (3), 29-41. DOI: https://doi.org/10.32523/2077-9879-2021-12-3-29-41

Борубаев, А.А., Равномерная топология. [Текст]/ Борубаев А.А.// Бишкек. Илим, 2013.-338 с.

Michael, E. Topologies on spaces of supsets[Теxt]/ Michael. E. // Trans. Amer. Math. Soc. – 1951. – № 1 (71). – P. 152-172. DOI: https://doi.org/10.1090/S0002-9947-1951-0042109-4

Борубаев, А.А. Равномерные пространства и равномерно непрерывные отображения. [Текст]/ Борубаев А.А. // – Фрунзе: Илим, 1990.-172 с.

Downloads

Published

2023-06-30

How to Cite

Beshimov , R., & Safarova , D. (2023). SOME PROPERTIES UNIFORM SPACE AND ITS HYPERSPACE. Journal of Osh State University. Mathematics. Physics. Technical Sciences, (1(2), 281–286. https://doi.org/10.52754/16948645_2023_1_281