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.