Symmetrically continuous functions on various subsets of the real line


Marcin Szyszkowski

Real Anal. Exchange 25(2) (1999-2000), 547-564.

We define symmetric continuity for functions defined on arbitrary subsets of 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.

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Last modified November 28, 2000.