Coursera Complex Analysis 1.5 Terminology

Jul 4, 2016

B_r(z_0) disk radius r, centre z_0, excluding boundary. |z - z_0| < r

K_r(z_0) circle radius r, centre z_0, . |z - z_0| = r

Interior point. E is some subset of the complex plane. z_0 is an interior point of E if there is some r > 0 such that the disc around z_0 is in E, i.e. B_r(z_0) \subset E .

Boundary point. E is some subset of the complex plane. b is a boundary point of E if every disc around b contains a point in E and a point not in E.

The set of all boundary points is \partial E.

A set is open if every one of its points are interior.

A set is closed if it contains all its boundary points.

Closure

Interior

 

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