Categorical and cardinal properties of hyperspaces with a finite number of components. (English. Russian original) Zbl 1442.18007
J. Math. Sci., New York 245, No. 3, 390-397 (2020); translation from Itogi Nauki Tekh., Ser. Sovrem. Mat. Prilozh., Temat. Obz. 144, 96-103 (2018).
Summary: In this paper, we examine categorical and cardinal properties of hyperspaces with finite number of components. We prove that the functor \(C_n : \operatorname{Comp} \rightarrow \operatorname{Comp}\) 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 \(C_n(X)\).
MSC:
| 18B20 | Categories of machines, automata |
| 46E27 | Spaces of measures |
| 54B30 | Categorical methods in general topology |
| 54B20 | Hyperspaces in general topology |
| 54A25 | Cardinality properties (cardinal functions and inequalities, discrete subsets) |
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