A sufficient condition for quasi-metrizability of a topological space

Norman, Lester J.

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The quasi topology associated with a countably subadditive set function

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This is a general study of an increasing, countably subadditive set function, called a capacity, and defined on the subsets of a topological space $X$ . The principal aim is the study of the “quasi-topological” properties of subsets of $X$ , or of numerical functions on $X$ , with respect to such a capacity $C$ . Analogues are obtained to various important properties of the fine topology in potential theory, notably the quasi Lindelöf principle (Doob), the existence of a fine support (Getoor), and...