On Kantorovih's result on the symmetry of Dini derivatives
Comment.Math.Univ.Carolin. 51,4 (2010)619{629.
Abstrat:Forf:(a;b)!R,letA
f
bethesetofpointsatwhihf isLipshitzfromthe
leftbutnotfromtheright. L.V.Kantorovih(1932)provedthat,iff isontinuous,then
A
f
is a\(k
d
)-reduibleset". Theproofs of L.Zajek(1981) and B.S.Thomson (1985)
givethatAf isa-stronglyrightporous setforanarbitraryf. Wedisussonnetions
betweenthesetworesults. Themainmotivationforthepresentnotewastheobservation
thatKantorovih'sresultimpliestheexisteneofa-stronglyrightporoussetA(a;b)
forwhihnoontinuousfwithAAfexists. UsingThomson'sproof,weprovethatsuh
ontinuousf (resp.anarbitraryf) existsifandonlyifthereexiststronglyright porous
setsAnsuhthatAn%A. Thisharaterizationimprovesbothresultsmentionedabove.
Keywords:Diniderivative,one-sidedLipshitzness, -porousset,strongrightporosity,
abstratporosity
AMSSubjetClassiation:26A27,28A05
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