Is that the reason why $C^{0}$ being topological manifold due to that $C^{0}=\phi$ which contains nothing? Correct me if I am wrong. I am new to differential topology.
2026-04-02 06:39:44.1775111984
About $C^{0}$ being topological manifold
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No, $C^0$ denotes the ring of continuous functions, as opposed to $C^k$, $k\ge 1$, which denotes functions with up to $k$th order derivatives continuous.