Real Analysis Exchange

Porosity in Spaces of Darboux-Like Functions

Harvey Rosen

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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.

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

First available in Project Euclid: 2 January 2009

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

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


Rosen, Harvey. Porosity in Spaces of Darboux-Like Functions. Real Anal. Exchange 26 (2000), no. 1, 195--200.

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