Real Analysis Exchange

Sierpinski-Zygmund uniform limits of extendable connectivity functions .

Harvey Rosen

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We show that the class $SZ$ of Sierpinski-Zygmund functions has a nonempty intersection with the class $\extb$ of all uniform limits of sequences of extendable connectivity functions $f_n:\R\to\R.$ We reconsider the idea of $f$-negligible sets this time with respect to $f\in \extb.$ We also show that under MA, $SZ\cap \extb$ cannot be characterized by preimages of sets.

Article information

Real Anal. Exchange, Volume 28, Number 1 (2002), 105-110.

First available in Project Euclid: 12 June 2006

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Mathematical Reviews number (MathSciNet)

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

Sierpinski-Zygmund function uniform limit of extendable connectivity functions negligible set characterization by preimages


Rosen, Harvey. Sierpinski-Zygmund uniform limits of extendable connectivity functions . Real Anal. Exchange 28 (2002), no. 1, 105--110.

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