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Suppose $M$ is a Topological Space. We say $M$ is a Topological Manifold with Manifold Dimension $n$ if

1. $M$ is a Hausdorff
2. $M$ is a Second Countable
3. $M$ is Locally Euclidean of Manifold Dimension $n$

1. Graphs of Continuous Functions are Topological Manifolds