Real Analysis Exchange

Porosity of the Extendable Connectivity Function Space

Harvey Rosen

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

https://projecteuclid.org/euclid.rae/1212412848

Mathematical Reviews number (MathSciNet)
MR1922661

Zentralblatt MATH identifier
1047.26002

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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