Geodesic
Uniform space and its hyperspace
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Geometry and topology, Tome 197 (2021), pp. 108-116

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In this paper, we examine some topological properties of uniform spaces and their hyperspaces. We prove that a uniform space $(X,\mathscr{U})$ is uniformly precompact if and only if $ (\exp_{c}X, \exp_{c}\mathscr{U})$ is uniformly precompact. Also we prove that the uniform hyperspace $(\exp_{c}X, \exp_{c} \mathscr{U})$ preserves uniformly local compactness, uniform connection, uniform paracompactness, and uniform $R$-paracompactness.
Keywords: uniform space, uniformity, uniformly connected space, uniformly paracompact space, uniformly $R$-paracompact space. 
@article{INTO_2021_197_a12,
     author = {R. B. Beshimov and D. T. Safarova},
     title = {Uniform space and its hyperspace},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {108--116},
     publisher = {mathdoc},
     volume = {197},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2021_197_a12/}
}
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R. B. Beshimov; D. T. Safarova. Uniform space and its hyperspace. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Geometry and topology, Tome 197 (2021), pp. 108-116. http://geodesic.mathdoc.fr/item/INTO_2021_197_a12/