On Compactness with Respect to Countable Extensions of Ideals and the Generalized Banach Category Theorem |
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| Authors: | J Dontchev M Ganster |
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| Institution: | (1) Department of Mathematics, University of Helsinki, PL 4, Yliopistonkatu 5, 00014 Helsinki, Finland E-mail;(2) Department of Mathematics, Graz University of Technology, Steyrergasse 30, A-8010 Graz, Austria E-mail |
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| Abstract: | We extend a theorem of Hamlett and Jankovi by proving that if a topological space (X,  ) is compact with respect to the countable extension of I, then the local function A
*(I) of every subset A of X with respect to and I is a compact subspace with respect to the extension  in A
* (I). We also give a generalized version of the Banach category theorem. |
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