Manifold
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The Möbius strip is an example of a 2-manifold.
An n-dimensional manifold (or n-manifold) M is a topological space such that every point in M has a neighbourhood that is homeomorphic to Rn.
An n-dimensional complex manifold N is a topological space such that every point in N has a neighbourhood that is homeomorphic to Cn.
Manifolds are Hausdorff and 2nd-countable.