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
Format: Artikel
Sprache:eng
Schlagworte:
Hyperspaces
Mathematics
Mathematics and Statistics
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Zusammenfassung: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 ).
ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-020-04701-8