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.
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The author was supported by grants VEGA 1/0002/12 and APVV-0269-11.
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Repický, M. Sets of points of symmetric continuity. Arch. Math. Logic 54, 803–824 (2015). https://doi.org/10.1007/s00153-015-0441-z
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DOI: https://doi.org/10.1007/s00153-015-0441-z