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A characterization of almost resolvable spaces

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Abstract

A space is said to be resolvable if it has two disjoint dense subsets. It is shown thatX is a Baire space with no resolvable open subsets iff every real function defined onX has a dense set of points of continuity. Thus almost resolvable spaces, as defined by Bolstein, are shown to be characterized as the union of a first category set and a closed resolvable set.

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Authors and Affiliations

  1. Department of Mathematics, University of Missouri-Kansas City, 64110, Kansas City, MO

    James Foran & Paul Liebnitz

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  1. James Foran
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  2. Paul Liebnitz
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Foran, J., Liebnitz, P. A characterization of almost resolvable spaces. Rend. Circ. Mat. Palermo 40, 136–141 (1991). https://doi.org/10.1007/BF02846366

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  • DOI: https://doi.org/10.1007/BF02846366

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