Some Topological Properties of a Functor of Finite Degree
R. B. BeshimovNational University of Uzbekistan named after M. Ulugbek, Department of Geometry and Topology, 100174, Tashkent, UzbekistanDilnora SafarovaNational University of Uzbekistan named after M. Ulugbek, Department of Geometry and Topology, 100174, Tashkent, Uzbekistan
ABI
Аннотация
In this paper, the connection between a finally compact, pceudocompact, extremely disconnected, $$\aleph$$ -space and its hyperspace is studied. The action of functors $$\exp_{n},\exp_{c},\exp$$ on finally compact, pceudocompact, extremely disconnected and $$\aleph$$ -spaces is investigated. Some topological properties of uniformly space and its hyperspace is studied. It is proved: if the uniform space $$(X,\mathcal{U})$$ is uniformly paracompact, then $$\left(\exp_{c}X,\exp_{c}\mathcal{U}\right)$$ is uniformly paracompact. It is also shown: if the uniform space $$(X,\mathcal{U})$$ is uniformly $$R$$ -paracompact, then a uniform space $$\left(\exp_{c}X,\exp_{c}\mathcal{U}\right)$$ is uniformly $$R$$ -paracompact.
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