Categorical and Cardinal Properties of Hyperspaces with a Finite Number of Components

Categorical and Cardinal Properties of Hyperspaces with a Finite Number of Components

In this paper, we examine categorical and cardinal properties of hyperspaces with finite number of components. We prove that the functor C n : Comp → Comp is not normal, i.e., it does not preserve epimorphisms of continuous mappings. We also discuss the density, the caliber, and the Shanin number of...

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Veröffentlicht in:Journal of mathematical sciences (New York, N.Y.) N.Y.), 2020-03, Vol.245 (3), p.390-397
Hauptverfasser: Beshimov, R. B., Mamadaliev, N. K., Eshtemirova, Sh. Kh
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Hyperspaces
Mathematics
Mathematics and Statistics
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creator Beshimov, R. B.
Mamadaliev, N. K.
Eshtemirova, Sh. Kh
description In this paper, we examine categorical and cardinal properties of hyperspaces with finite number of components. We prove that the functor C n : Comp → Comp is not normal, i.e., it does not preserve epimorphisms of continuous mappings. We also discuss the density, the caliber, and the Shanin number of the space C n ( X ).
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subjects Hyperspaces
Mathematics
Mathematics and Statistics
title Categorical and Cardinal Properties of Hyperspaces with a Finite Number of Components
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