## Real Analysis Exchange

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

Hongjian Shi

#### 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