View source for Non-singular boundary point

<!--
n0672901.png
$#A+1 = 18 n = 0
$#C+1 = 18 : ~/encyclopedia/old_files/data/N067/N.0607290 Non\AAhsingular boundary point,
Automatically converted into TeX, above some diagnostics.
Please remove this comment and the {{TEX|auto}} line below,
if TeX found to be correct.
-->

{{TEX|auto}}
{{TEX|done}}

''regular boundary point''

An accessible boundary point (cf. [[Attainable boundary point|Attainable boundary point]])  $  \zeta $
of the domain of definition  $  D $
of a single-valued analytic function  $  f ( z) $
of a complex variable  $  z $
such that  $  f ( z ) $
has an [[Analytic continuation|analytic continuation]] to  $  \zeta $
along any path inside  $  D $
to  $  \zeta $. 
In other words, a non-singular boundary point is accessible, but not singular. See also [[Singular point|Singular point]] of an analytic function.

====Comments====
Note that the same point in the boundary of  $  D $
may give rise to several different accessible boundary points, some of which may be singular, others regular. E.g., consider the domain  $  D = \mathbf C \setminus  ( - \infty , 0 ] $, 
and the function  $  f ( z) = ( h ( z) - \pi i )  ^ {-} 1 $, 
where  $  h $
is the principal value of  $   \mathop{\rm log}  z $. 
Then  "above"   $  - 1 $
there are two accessible boundary points: one singular, corresponding to approach along  $  z = - 1 + i t $, 
$  0 \leq  t \leq  1 $; 
one regular, corresponding to approach along  $  z = - 1 - i t $, 
$  0 \leq  t \leq  1 $.

====References====
<table><TR><TD valign="top">[a1]</TD> <TD valign="top">  A.I. Markushevich,   "Theory of functions of a complex variable" , '''3''' , Chelsea  (1977)  pp. Chapts. 2; 8  (Translated from Russian)</TD></TR></table>