May 2024
Intermediate to advanced
481 pages
17h 15m
English
Content preview from Complex Analysis
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“ca: chapter_01” — 2012/3/27 — 20:27 — page 36 — #36
36
|
Complex Analysis
1.12.4 Neighbourhood of a Point
The set of points given by S =
{
z ∈ C:
|
z − z
0
|
<δ, δ>0
}
is known as a neighbourhood or a circular
neighbourhood of a point z
0
in the complex plane. It is denoted by N
δ
(
z
0
)
. In other words, neighbourhood
consists of all points z lying inside but not on a circle centred at z
0
and with a specified positive radius δ.
A deleted neighbourhood of z
0
is the set of points given by
{
z ∈ C:0<
|
z − z
0
|
<δ
}
, i.e.
neighbourhood of z
0
where z
0
is omitted. It is denoted by N
δ
(
z
0
)
\z
0
.
The set of numbers z such that
|
z
|
> k, where k is any positive real number is called a neighbourhood ...
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