simple boundary point


Let G be a region and ωG (the boundary of G). Then we call ω a simple boundary point if whenever {ωn}G is a sequence converging to ω there is a path γ:[0,1] such that γ(t)G for 0t<1, γ(1)=ω and there is a sequence {tn}[0,1) such that tn1 and γ(tn)=ωn for all n.

For example if we let G be the open unit discPlanetmathPlanetmath, then every boundary point is a simple boundary point. This definition is useful for studying boundary behaviour of Riemann maps (maps arising from the Riemann mapping theoremMathworldPlanetmath), and one can prove for example the following theorem.


Suppose that GC is a boundedPlanetmathPlanetmathPlanetmath simply connected region such that every point in the boundary of G is a simple boundary point, then G is a Jordan curve.


  • 1 John B. Conway. . Springer-Verlag, New York, New York, 1995.
Title simple boundary point
Canonical name SimpleBoundaryPoint
Date of creation 2013-03-22 14:23:23
Last modified on 2013-03-22 14:23:23
Owner jirka (4157)
Last modified by jirka (4157)
Numerical id 5
Author jirka (4157)
Entry type Definition
Classification msc 30-00
Classification msc 54-00