Real Analysis Exchange

Weakly Symmetric Functions and Weakly Symmetrically Continuous Functions

Kandasamy Muthuvel

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We prove that there exists a nowhere weakly symmetric function $f: \mathbb{R} \rightarrow \mathbb{R}$ that is everywhere weakly symmetrically continuous and everywhere weakly continuous. Existence of a nowhere weakly symmetrically continuous function $f: \mathbb{R} \rightarrow \mathbb{R}$ that is everywhere weakly symmetric remains open.

Article information

Real Anal. Exchange, Volume 40, Number 2 (2015), 455-458.

First available in Project Euclid: 4 April 2017

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Mathematical Reviews number (MathSciNet)

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} 26A21: Classification of real functions; Baire classification of sets and functions [See also 03E15, 28A05, 54C50, 54H05]
Secondary: 26A05

weakly symmetrically continuous function weakly symmetric function


Muthuvel, Kandasamy. Weakly Symmetric Functions and Weakly Symmetrically Continuous Functions. Real Anal. Exchange 40 (2015), no. 2, 455--458.

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