Real Analysis Exchange

Some typical properties of symmetrically continuous functions, symmetric functions and continuous functions

Hongjian Shi

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Abstract

In this paper we show that the typical symmetrically continuous function and the typical symmetric function have \(c\)-dense sets of points of discontinuity. Also we show the existence of a nowhere symmetrically differentiable function and a nowhere quasi-smooth function by showing directly such functions are typical in the space of all real continuous functions.

Article information

Source
Real Anal. Exchange, Volume 21, Number 2 (1995), 708-714.

Dates
First available in Project Euclid: 14 June 2012

Permanent link to this document
https://projecteuclid.org/euclid.rae/1339694099

Mathematical Reviews number (MathSciNet)
MR1407283

Zentralblatt MATH identifier
0879.26009

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} 26A27: Nondifferentiability (nondifferentiable functions, points of nondifferentiability), discontinuous derivatives

Keywords
symmetrically continuous function symmetric function continuous function nowhere symmetrically differentiable function nowhere quasi-smooth function

Citation

Shi, Hongjian. Some typical properties of symmetrically continuous functions, symmetric functions and continuous functions. Real Anal. Exchange 21 (1995), no. 2, 708--714. https://projecteuclid.org/euclid.rae/1339694099


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