Real Analysis Exchange

Generalizing the Blumberg Theorem

Francis Jordan

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Given a collection of functions of some class defined on the real line, when can you find a large set upon which the restriction of every function is continuous? We consider this problem (and related problems) for various classes of functions and various notions of largeness. These problems can be considered in terms of finding the covering, uniformity (non), additivity, and cofinality numbers for some ideal-like collections of sets.

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Real Anal. Exchange, Volume 27, Number 2 (2001), 423-440.

First available in Project Euclid: 2 June 2008

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Zentralblatt MATH identifier

Primary: 26A15: Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.) {For properties determined by Fourier coefficients, see 42A16; for those determined by approximation properties, see 41A25, 41A27} 54A25: Cardinality properties (cardinal functions and inequalities, discrete subsets) [See also 03Exx] {For ultrafilters, see 54D80}

cardinal functions meager sets Baire class 1 Baire property


Jordan, Francis. Generalizing the Blumberg Theorem. Real Anal. Exchange 27 (2001), no. 2, 423--440.

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