# Non-singular boundary point

*regular boundary point*

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

#### Comments

Note that the same point in the boundary of may give rise to several different accessible boundary points, some of which may be singular, others regular. E.g., consider the domain , and the function , where is the principal value of . Then "above" there are two accessible boundary points: one singular, corresponding to approach along , ; one regular, corresponding to approach along , .

#### References

[a1] | A.I. Markushevich, "Theory of functions of a complex variable" , 3 , Chelsea (1977) pp. Chapts. 2; 8 (Translated from Russian) |

**How to Cite This Entry:**

Non-singular boundary point. E.D. Solomentsev (originator),

*Encyclopedia of Mathematics.*URL: http://www.encyclopediaofmath.org/index.php?title=Non-singular_boundary_point&oldid=13119