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- W2143172396 abstract "In [Evans, Humke and O'Malley, J. Appl. Anal. 6: 1–16, 2000], the present authors and Richard O'Malley showed that in order for a function be universally polygonally approximable it is necessary that for each ε > 0, the set of points of non-quasicontinuity be σ – (1 – ε) symmetrically porous. The question as to whether that condition is sufficient or not was left open. Here we prove that if a set, , such that each Ei is closed and 1-symmetrically porous, then there is a universally polygonally approximable function, ƒ, whose set of points of non-quasicontinuity is precisely E. Although it is tempting to call this a partial converse to our earlier theorem it might be more since it is not known if these two notions of symmetric porosity differ in the class of Fσ sets." @default.
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- W2143172396 date "2001-01-01" @default.
- W2143172396 modified "2023-10-18" @default.
- W2143172396 title "Exceptional Sets for Universally Polygonally Approximable Functions" @default.
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- W2143172396 doi "https://doi.org/10.1515/jaa.2001.175" @default.
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