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2015 Weakly Symmetric Functions and Weakly Symmetrically Continuous Functions
Kandasamy Muthuvel
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Real Anal. Exchange 40(2): 455-458 (2015).

Abstract

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.

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Kandasamy Muthuvel. "Weakly Symmetric Functions and Weakly Symmetrically Continuous Functions." Real Anal. Exchange 40 (2) 455 - 458, 2015.

Information

Published: 2015
First available in Project Euclid: 4 April 2017

zbMATH: 1384.26018
MathSciNet: MR3499777

Subjects:
Primary: 26A15 , 26A21
Secondary: 26A05

Keywords: weakly symmetric function , weakly symmetrically continuous function

Rights: Copyright © 2015 Michigan State University Press

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Vol.40 • No. 2 • 2015
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