A visual explanation and definition of manifolds are given. This includes motivations for topology, Hausdorffness and second-countability.

If you want to learn more, check out one of these (or any other basic differential geometry or topology book):

- M. Spivak: "A Comprehensive Introduction to Differential Geometry"
- M. Nakahara: "Geometry, Topology and Physics"
- J. W. Milnor: "Topology from the differentiable viewpoint"

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