Wyniki wyszukiwania - BazTech

Ograniczanie wyników

1 Journal of Applied Analysis

1 2001

Znaleziono wyników: 1

Liczba wyników na stronie

Wyniki wyszukiwania

Wyszukiwano:
w słowach kluczowych: interpolate

Sortuj według:

Ogranicz wyniki do:

Exceptional sets for universally polygonally approximable functions

Evans M. J., Humke P. D.

Journal of Applied Analysis

2001

Vol. 7, nr 2

175-190

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.