Attainable boundary arc
From Encyclopedia of Mathematics
of a domain 
in the 
-plane
A Jordan arc forming part of the boundary of 
and at the same time forming part of the boundary of some Jordan domain 
. Each point on an attainable boundary arc is an attainable (from the inside of 
) boundary point of 
(cf. Attainable boundary point). A conformal mapping of a simply-connected domain 
onto the unit disc 
: 
can be continuously extended to the non-terminal points of an attainable boundary arc to a homeomorphism of the open attainable boundary arc onto some open arc of the circle 
.
Comments
The standard Western terminology is accessible boundary arc and accessible boundary point, see e.g. [a1].
References
| [a1] | E.F. Collingwood, A.J. Lohwater, "The theory of cluster sets" , Cambridge Univ. Press (1966) pp. Chapt. 9 |
| [a2] | A.I. Markushevich, "Theory of functions of a complex variable" , 3 , Chelsea (1977) pp. Chapt. 2 (Translated from Russian) |
How to Cite This Entry:
Attainable boundary arc. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Attainable_boundary_arc&oldid=36924
Attainable boundary arc. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Attainable_boundary_arc&oldid=36924
This article was adapted from an original article by E.P. Dolzhenko (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article