## Real Analysis Exchange

### A symmetrically continuous function which is not countably continuous

#### Abstract

We construct a symmetrically continuous function $f\colon\mathbb{R}\to\mathbb{R}$ such that for some $X\subset\mathbb{R}$ of cardinality continuum $f|X$ is of Sierpiński-Zygmund type. In particular such an $f$ is not countably continuous. This gives an answer to a question of Lee Larson.

#### Article information

Source
Real Anal. Exchange, Volume 22, Number 1 (1996), 428-432.

Dates
First available in Project Euclid: 1 June 2012