N-point Virasoro algebras are multi-point Krichever--Novikov type algebras

We show how the recently again discussed $N$-point Witt, Virasoro,
and affine Lie
algebras are genus zero
examples of the multi-point versions of Krichever--Novikov
type
algebras as introduced and studied by Schlichenmaier. Using this more
general point of view, useful structural insights and an easier access to
calculations
can be obtained. The concept of almost-grading will yield information
about
triangular decompositions
which are of importance in the theory of representations.
As examples the algebra of functions,
vector fields, differential operators, current algebras, affine Lie
algebras, Lie superalgebras
and their
central extensions are studied. Very detailed calculations
for the three-point case are given.