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On a weakly closed subset of the space of $\tau $-smooth measures

1974
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Proceedings of the American Mathematical Society
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It is known that a lot of topological properties devolve from a basic space X to the family MT(X) of all r-smooth Borel measures endowed with the weak topology (or to certain subspaces of Mr(X)). The aim of this paper is to show that among these topological properties there cannot be properties which are hereditary on closed subsets but not on countable products of X, e.g. normality, paracompactness, the Lindelöf property, local compactness and d-compactness. For this purpose it is proved that

doi:10.1090/s0002-9939-1974-0338758-7
fatcat:qtvzc56wj5h4fjfahqx2epjg5q