![]() ![]() ![]() Typically, access is provided across an institutional network to a range of IP addresses. If you are a member of an institution with an active account, you may be able to access content in one of the following ways: Get help with access Institutional accessĪccess to content on Oxford Academic is often provided through institutional subscriptions and purchases. In the course of the paper some generalizations are given of results of the Robertsons in on spaces of compact, “ weakly ” compact and “ weakly ” relatively compact subsets. The final section is an investigation of hyperspaces arising from two uniformities on a set, associated in a certain way. §3 contains some applications to linear spaces and in particular to completions of quotient spaces. ![]() The study is extended in §2 to hyperspaces consisting of compact, precompact, relatively compact and finite sets. Thus Theorem 1 says that there is a natural isomorphism between the functors π E and π Eπ, where EX is the space of non-empty closed subsets of X, endowed with the Hausdorff uniformity, and this result is applied to a consideration of which spaces have hypercompletions, to the question of compactifications of hyperspaces, and to finding when the Hausdorff uniformity is compatible with the finite (Vietoris) topology. We consider the uniform hyperspaces of a uniform space X, its associated Hausdorff space sX and its Hausdorff completion π X, and investigate the relationships between the functors s and π and the various hyperspace functors. ![]()
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