## Real Analysis Exchange

### Weakly Symmetric Functions and Weakly Symmetrically Continuous Functions

Kandasamy Muthuvel

#### 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.

#### Article information

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

Dates
First available in Project Euclid: 4 April 2017