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Continuum theory, point-set topology, spaces with algebraic structure, foundations, dimension theory, local and global properties.

10 votes
1 answer
1k views

Open (resp., closed) balls homeomorphic to open (resp., closed) discs on the plane

Let $\Sigma$ be a compact (smooth) surface, with a geodesic metric $d$ (compatible with the topology of $\Sigma$). Let $x \in \Sigma$, and suppose you have the following: for every $r<1$, the open ba …
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