Definition:Neighborhood (Complex Analysis)

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This page is about neighborhoods in the complex plane. For other uses, see Definition:Neighborhood.

Definition

Let $z_0 \in \C$ be a complex number.

Let $\epsilon \in \R_{>0}$ be a (strictly) positive real number.


The $\epsilon$-neighborhood of $z_0$ is defined as:

$\map {N_\epsilon} {z_0} := \set {z \in \C: \cmod {z - z_0} < \epsilon}$


Also known as

A neighborhood in this context is often referred to as an open disk (UK spelling: open disc).


Some sources introduce this concept as $\delta$-neighborhood (that is: delta), but it is the same thing.


Also see


Linguistic Note

The UK English spelling of neighborhood is neighbourhood.


Sources