Real Analysis Exchange

Porosity in Spaces of Darboux-Like Functions

Harvey Rosen

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Abstract

It is known that the six Darboux-like function spaces of continuous, extendable, almost continuous, connectivity, Darboux, and peripherally continuous functions $f\:R\to \R$, with the metric of uniform convergence, form a strictly increasing chain of subspaces. We denote these spaces by \C, \E, \AC, \Conn, \D, and \PC, respectively. We show that C and D are porous and AC and Conn are not porous in their successive spaces of this chain.

Article information

Source
Real Anal. Exchange, Volume 26, Number 1 (2000), 195-200.

Dates
First available in Project Euclid: 2 January 2009

Permanent link to this document
https://projecteuclid.org/euclid.rae/1230939153

Mathematical Reviews number (MathSciNet)
MR1825503

Zentralblatt MATH identifier
1035.26004

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} 54C08: Weak and generalized continuity 54C35: Function spaces [See also 46Exx, 58D15]

Keywords
porosity spaces of continuous extendable almost continuous connectivity Darboux peripherally continuous functions

Citation

Rosen, Harvey. Porosity in Spaces of Darboux-Like Functions. Real Anal. Exchange 26 (2000), no. 1, 195--200. https://projecteuclid.org/euclid.rae/1230939153


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