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On inductively open real functions


Author: Biagio Ricceri
Journal: Proc. Amer. Math. Soc. 90 (1984), 485-487
MSC: Primary 54C10; Secondary 54C30
DOI: https://doi.org/10.1090/S0002-9939-1984-0728374-3
MathSciNet review: 728374
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Abstract: In this note, given a locally connected topological space $ X$, we characterize those continuous and locally nonconstant real functions on $ X$ which are inductively open there.


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  • [1] A. Arhangel′skiĭ, On open and almost-open mappings of topological spaces, Dokl. Akad. Nauk SSSR 147 (1962), 999–1002 (Russian). MR 0143179
  • [2] Biagio Ricceri, Sur la semi-continuité inférieure de certaines multifonctions, C. R. Acad. Sci. Paris Sér. I Math. 294 (1982), no. 7, 265–267 (French, with English summary). MR 653748
  • [3] Biagio Ricceri and Alfonso Villani, Openness properties of continuous real functions on connected spaces, Rend. Mat. (7) 2 (1982), no. 4, 679–687 (1983). MR 699444
  • [4] Biagio Ricceri, Applications de théorèmes de semi-continuité inférieure, C. R. Acad. Sci. Paris Sér. I Math. 295 (1982), no. 2, 75–78 (French, with English summary). MR 676366
  • [5] Biagio Ricceri, Solutions lipschitziennes d’équations différentielles sous forme implicite, C. R. Acad. Sci. Paris Sér. I Math. 295 (1982), no. 3, 245–248 (French, with English summary). MR 681589

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DOI: https://doi.org/10.1090/S0002-9939-1984-0728374-3
Article copyright: © Copyright 1984 American Mathematical Society

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