1. Complex numbers A complex number z is defined as an ordered ...

Some topological definitions
• A point z0 is called an interior point of a set S if there exists a
neighborhood of z0 with all of these points belong to S.
• If every neighborhood of z0 contains points of S and also points
not belonging to S then z0 is called a boundary point.
• The set of all boundary points of a set S is called the boundary
of S. If a point is neither an interior nor a boundary point, then
it is called an exterior point of S.
Remark
If z0 is not a boundary point, then there exists a neighborhood of
z0 such that it is completely inside S or completely outside S. In
the former case, it is an interior point. In the latter case, it is an
exterior point.
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