Wikipedia
Pseudomanifold
A pseudomanifold is a special type of topological space. It looks like a manifold at most of the points, but may contain singularities. For example, the cone of solutions of z = x + y forms a pseudomanifold.
[[ torus.jpg|thumb|
A pinched torus
]] A pseudomanifold can be regarded as a combinatorial realisation of the general idea of a manifold with singularities. The concepts of orientability, orientation and degree of a mapping make sense for pseudomanifolds and moreover, within the combinatorial approach, pseudomanifolds form the natural domain of definition for these concepts.