Real Analysis Exchange

A new variant of Blumberg’s theorem

Aleksandra Katafiasz and Tomasz Natkaniec

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Abstract

We prove that for every real function \(f\) defined on a separable, complete and dense in itself metric space \(X\) there exists a \(c\)-dense set \(W\subset X\) such that \(f\upharpoonleft W\) is super quasi-continuous.

Article information

Source
Real Anal. Exchange, Volume 22, Number 2 (1996), 806-813.

Dates
First available in Project Euclid: 22 May 2012

Permanent link to this document
https://projecteuclid.org/euclid.rae/1337713161

Mathematical Reviews number (MathSciNet)
MR1460992

Zentralblatt MATH identifier
0889.26002

Subjects
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} 54C30: Real-valued functions [See also 26-XX]

Keywords
continuous function quasi-continuous function super quasi-continuous function cliquish function pointwise discontinuous function κ-Lusin set

Citation

Katafiasz, Aleksandra; Natkaniec, Tomasz. A new variant of Blumberg’s theorem. Real Anal. Exchange 22 (1996), no. 2, 806--813. https://projecteuclid.org/euclid.rae/1337713161


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References

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