Real Analysis Exchange

Porosity of the Extendable Connectivity Function Space

Harvey Rosen

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Let $I = [0,1]$, and let $Ext(I)$ or $Ext$ denote the subspace of all extendable connectivity functions $f:I \to {\mathbb R}$ with the metric of uniform convergence on $I^{\mathbb R}$. We show that $Ext$ is porous in the almost continuous function space $AC$ by showing that the space $AC \cap PR$ of all almost continuous functions with perfect roads is porous in $AC$. We also show that for $n >1$, the subspace $Ext({\mathbb R}^n)$ of all extendable connectivity functions $f:{\mathbb R}^n \to {\mathbb R}$ is a boundary set in the Darboux function space $D({\mathbb R}^n)$.

Article information

Real Anal. Exchange, Volume 27, Number 2 (2001), 457-462.

First available in Project Euclid: 2 June 2008

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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} 54C35: Function spaces [See also 46Exx, 58D15] 54C30: Real-valued functions [See also 26-XX]

porous set boundary set spaces of extendable connectivity functions almost continuous functions with perfect roads Darboux functions


Rosen, Harvey. Porosity of the Extendable Connectivity Function Space. Real Anal. Exchange 27 (2001), no. 2, 457--462.

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