View source for Attainable boundary arc

''of a domain $G$ in the $z$-plane''

A Jordan arc forming part of the boundary of $G$ and at the same time forming part of the boundary of some Jordan domain $g \subset G$. Each point on an attainable boundary arc is an attainable (from the inside of $g$) boundary point of $G$ (cf. [[Attainable boundary point]]). A conformal mapping of a simply-connected domain $G$ onto the unit disc $D = \{ z : |z| < 1 \}$ 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 $|z| = 1$.



====Comments====
The standard Western terminology is accessible boundary arc and accessible boundary point, see e.g. [[#References|[a1]]].

====References====
<table>
<TR><TD valign="top">[a1]</TD> <TD valign="top">  E.F. Collingwood,   A.J. Lohwater,   "The theory of cluster sets" , Cambridge Univ. Press  (1966)  pp. Chapt. 9</TD></TR>
<TR><TD valign="top">[a2]</TD> <TD valign="top">  A.I. Markushevich,   "Theory of functions of a complex variable" , '''3''' , Chelsea  (1977)  pp. Chapt. 2  (Translated from Russian)</TD></TR>
</table>

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