By the inequality $ | z-z_ {0} | <\ rho $ plane defined point set is to $ z_ {0} $ for the heart, a circle with radius $ \ $ of Rho.
Called dot $ z_ {0} $ a $ \ rho $ - neighborhood , often referred to as $ N _ {\ rho} ( z_ {0}) $, and said $ 0 <| z-z_ { 0} | <\ rho point $ $ z_ {0} $ of the neighborhood to the heart, often referred to as $ N _ {\ rho} ( z_ {0}) - \ {z_ {0} \} $.
Poly point: infinite number of points at any point on the plane when the neighborhood of $ z_ {0} $ (not necessarily belonging to E) has the E, called $ z_ {0} is E $ accumulation point or limit point.
Outlier: $ z_ {0} $ E belongs to, but not the accumulation point E, called $ z_ {0} $ is an isolated point of E
An outer point: if $ z_ {0} $ does not belong to E, and E is not a point of the poly
All poly point set point referred to as the set E E $ '$
If the set point for each accumulation point E belong to E, $ E '\ subseteq E $ E is called a closed set , if the point $ z_ {0} $ exists a neighborhood included within E, called $ z_ { } $ E 0 is the interior point .
If all points are points set E point within, called E is an open set .
If $ z_ {0} is a neighborhood of any point while all belonging to point E and point E does not belong, called $ z_ {0} $ E as the boundary point .
Point set consisting of all the boundary points of the set of points called E E of the boundary . Denoted as $ \ partial E $
Outlier all border points.
Bounded set: If the normal number of M, so that at any point in the $ z $ E, has $ | z | \ leq M $ .
Unbounded Sets
Some accumulation equivalent definitions:
1) $ z_ {0} $ E is the accumulation point or limit point
2) $ z_ {0} $ containing any one of an infinite number of neighborhood points of E
3) $ z_ {0} $ containing any one of a neighborhood of the point E is different from $ z_ {0} $ of
4) $ z_ {0} $ a neighborhood containing any two points in E
5) may be removed from the E converges to $ z_ {0} $ point sequence
Region : open set 1, 2 either in full fold line connecting any two points in D.
Closed field: D plus his area boundary C
Area is open and does not contain boundary points.