On tightness-type properties of the space of weakly additive functionals. (English. Russian original) Zbl 07881422
Proc. Steklov Inst. Math. 324, 18-32 (2024); translation from Tr. Mat. Inst. Steklova 324, 24-38 (2024).
In this paper, the authors study tightness-type properties like tightness, minitightness, and local density of the space \(O_n(X)\) of weakly additive functionals with finite support. They also present an extension of the functor \(O_n\) of weakly additive functionals with finite support to the class of strictly \(\tau\)-continuous mappings. They introduce two extensions of the categories Comp and Tych (of compact and Tychonoff spaces, respectively). Some of the main results of the paper state that the functor \(O_n\) preserves the tightness character of infinite compact spaces and the local densities of the spaces \(X\) and \(O_n(X)\) coincide for any infinite compact space \(X\).
Reviewer: Dimitrios Georgiou (Pátra)
MSC:
| 54A25 | Cardinality properties (cardinal functions and inequalities, discrete subsets) |
| 54C35 | Function spaces in general topology |
| 46J10 | Banach algebras of continuous functions, function algebras |
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