Real Analysis Exchange

Porosity of the Extendable Connectivity Function Space

Harvey Rosen

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Abstract

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

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

Dates
First available in Project Euclid: 2 June 2008

Permanent link to this document
https://projecteuclid.org/euclid.rae/1212412848

Mathematical Reviews number (MathSciNet)
MR1922661

Zentralblatt MATH identifier
1047.26002

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

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

Citation

Rosen, Harvey. Porosity of the Extendable Connectivity Function Space. Real Anal. Exchange 27 (2001), no. 2, 457--462. https://projecteuclid.org/euclid.rae/1212412848


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