Symmetric behavior in functions
Author:
Udayan B. Darji
Journal:
Proc. Amer. Math. Soc. 119 (1993), 915923
MSC:
Primary 26A15; Secondary 26A24, 54C08
MathSciNet review:
1172958
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Abstract: S. Marcus raised the following problem: Find necessary and sufficient conditions for a set to be the set of points of symmetric continuity of some function . We show that there is no such characterization of topological nature. We prove that given a zerodimensional set , there exists a function whose set of points of symmetric continuity is topologically equivalent to . Thus, there is no "upper bound" on the topological complexities of . We also prove similar theorems about the set of points where a function may be symmetrically differentiable, symmetric, or smooth.
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029939199311729583
PII:
S 00029939(1993)11729583
Keywords:
Symmetric continuity,
symmetric derivative,
smooth,
perfect linearly independent sets,
the Baire property,
Borel functions,
coanalytic sets
Article copyright:
© Copyright 1993
American Mathematical Society
