Abstract
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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ACKNOWLEDGMENTS
The authors are grateful to the T. K. Yuldashev for helpful comments and advices.
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Beshimov, R.B., Safarova, D.T. Some Topological Properties of a Functor of Finite Degree. Lobachevskii J Math 42, 2744–2753 (2021). https://doi.org/10.1134/S1995080221120088
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DOI: https://doi.org/10.1134/S1995080221120088