A topological manifold is a locally Euclidean Hausdorff space. It is common to place additional requirements on topological manifolds. In particular, many authors define them to be paracompact or second-countable. The reasons, and some equivalent conditions, are discussed below.
In the remainder of this article a manifold will mean a topological manifold. An n-manifold will mean a topological manifold such that every point has a neighborhood homeomorphic to Rn.
Read more about Topological Manifold: Examples, Properties, Coordinate Charts, Classification of Manifolds, Manifolds With Boundary, See Also
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“As one who knows many things, the humanist loves the world precisely because of its manifold nature and the opposing forces in it do not frighten him. Nothing is further from him than the desire to resolve such conflicts ... and this is precisely the mark of the humanist spirit: not to evaluate contrasts as hostility but to seek human unity, that superior unity, for all that appears irreconcilable.”
—Stefan Zweig (18811942)