Exceptional sets for universally polygonally approximable functions

• Autorzy: Evans M. J. , Humke P. D.
• Języki publikacji: EN

Abstrakty

EN

In [9], the present authors and Richard O'Malley showed that in order for a function be universally polygonally approximate 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, E = U∞n=1 En, such that each Ei is closed and 1-symmetrically porous, then there is a universally polygonally approximable function, f, 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 F? sets.

Słowa kluczowe

EN

polygonal approximation; polygonally interpolate; interpolate; symmetric porosity; porous set

PL

zbliżenia wielokąta; wielomian interpolacyjny; interpolacyjny; porowatość symentryczna; porowaty zbiór

• Wydawca: De Gruyter
• Czasopismo: Journal of Applied Analysis
• Rocznik: 2001
• Tom: Vol. 7, nr 2
• Strony: 175--190
• Opis fizyczny: Bibliogr. 21 poz.

Twórcy

autor

Evans M. J.

• Department of Mathematics Washington and Lee University Lexington, Virginia 24450 U.S.A.

autor

Humke P. D.

• Department of Mathematics St. Olaf College Northfield, Minnesota 45701 U.S.A.

Bibliografia

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