  The Gelfand - Na\u{i}mark theorem supplies the one to one correspondence
between commutative $C^*$-algebras and locally compact Hausdorff spaces. So any
noncommutative $C^*$-algebra can be regarded as a generalization of a
topological space. Generalizations of several topological invariants can be
defined by algebraical methods. This article contains a pure algebraical
construction of inverse limits in the category of (noncommutative) covering
projections. It is proven that Moyal planes are inverse limits of covering
projections of noncommutative tori.
