×

zbMATH — the first resource for mathematics

Strict topology and perfect measures. (English) Zbl 0711.28002
The authors study several questions related with \(C_ b(X,E)\), the space of bounded continuous functions from a completely regular space X into a normed space over a field K \((=real\) or complex field). In the particular case where \(K=E={\mathbb{R}}\), they consider the topology \(\beta_ p\) [introduced by G. Koumoullis, Ill. J. Math. 26, 466-478 (1982; Zbl 0471.28003)] on \(C_ b(X,{\mathbb{R}})\) and its dual \(M_ p(X)\), the set of all scalar-valued Baire perfect measures on X. Results concerning Mackey and strongly Mackey spaces are proven.
Reviewer: O.T.Alas

MSC:
28A12 Contents, measures, outer measures, capacities
28A33 Spaces of measures, convergence of measures
46E10 Topological linear spaces of continuous, differentiable or analytic functions
46E27 Spaces of measures
PDF BibTeX XML Cite
Full Text: EuDML
References:
[1] W.W.Comfort S. Negrepontis: Continuous pseudometrics. Marcd Dekker, New York 1975. · Zbl 0306.54004
[2] L. Gilman M. Jerison: Rings of continuous functions. D. van Nostrand Co., Inc., New York 1960.
[3] S. S. Khurana: Topologies on spaces of vector-valued continuous functions. Trans. Amer. Math. Soc. 24 (1978) 195-211. · Zbl 0362.46035
[4] S. Choo S. S. Khurana: Strict topology and P-spaces. Proc. Arner. Math. Soc. 61 (1976) 280-284. · Zbl 0322.46052
[5] S. Khurana: Strict topology on paracompact locally compact spaces. Canad. J. Math. 29 (1977) 216, 219; Corrigendum 30 (1978) 671. · Zbl 0335.46007
[6] G. Koumoullis: Perfect, u-additive measures and strict topologies. Illinois J. Math. 26 (1982) 466-478. · Zbl 0471.28003
[7] H. H. Schaefer: Topological vector spaces. Macmillan, New York, 1966. · Zbl 0141.30503
[8] A. H. Schuchat: Integral representation theorems in topological vector spaces. Trans. Amer. Math. Soc. 172 (1972) 373-397. · Zbl 0231.46079
[9] F. D. Sentilles: Bounded continuous functions on completely regular spacess. Trans. Amer. Math. Soc. 168 (1912) 311-336.
[10] Robert Wheeler: The strict topology for P-spaces. Proc. Amer. Math. Soc. 41 (1973) 466-472. · Zbl 0272.46018
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.