Archive for Mathematical Logic

, Volume 54, Issue 7–8, pp 803–824 | Cite as

Sets of points of symmetric continuity

Article

Abstract

We study the sets of symmetric continuity of real functions in connection with the sets of continuity. We prove that sets of reals of cardinality \({ < \mathfrak{p}}\) and subsets of weakly independent \({G_\delta}\) sets of reals are sets of symmetric continuity. The latter strengthens a similar result of Darji. We improve results of Fried and Belna saying that the set of points of symmetric continuity of a real function that are not continuity points does not contain a nonmeager set with Baire property and has inner measure zero by introducing another notion of smallness below meager and measure zero.

Keywords

Real function Sets of symmetric continuity Weakly independent set Measure zero Meager 

Mathematics Subject Classification

Primary 03E15 Secondary 03E17 26A15 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Mathematical InstituteSlovak Academy of SciencesKosiceSlovak Republic

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