Symmetrically Continuous Functions on Various Subsets of the Real Line

Marcin Szyszkowski
Source: Real Anal. Exchange Volume 25, Number 2 (1999), 547-564.

Abstract

We define symmetric continuity for functions defined on arbitrary subsets of $\mathbb{R}$. The main result is that when a symmetrically continuous function is defined on a measurable set (a set with the Baire property), then it is continuous almost everywhere (on a residual set, respectively). This generalizes the known result for functions defined on the whole real line.

First Page:
Primary Subjects: 26A15
Full-text: Open access

Permanent link to this document: http://projecteuclid.org/euclid.rae/1230995392
Mathematical Reviews number (MathSciNet): MR1778510
Zentralblatt MATH identifier: 1016.26003

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