A complex manifold is a Hausdorff space
M which admits
a covering by open sets Uα each of
which is given with a homeomorphism
φα:Uα →
Vα ⊆ Cn
where n
may depend on α and each
Vα is an open subset of the ambient Euclidean
space. The coordinate charts must be compatible in the sense that where defined
the functions φβφ-1α are
holomorphic.
The dimension of M is the maximal n appearing as the ambient dimension
of one of its charts.
