Sets of points of symmetric continuity

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• 作者：Miroslav Repicky
• 关键词：Real function ; Sets of symmetric continuity ; Weakly independent set ; Measure zero ; Meager ; Primary 03E15 ; Secondary 03E17 ; 26A15
• 刊名：Archive for Mathematical Logic
• 出版年：2015
• 出版时间：November 2015
• 年：2015
• 卷：54
• 期：7-8
• 页码：803-824
• 全文大小：536 KB
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• 作者单位：Miroslav Repicky (1)
  
  1. Mathematical Institute, Slovak Academy of Sciences, Gre?ákova 6, 040 01, Kosice, Slovak Republic
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematical Logic and Foundations
  Mathematics
  Algebra
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1432-0665

文摘

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