Recent content by Laur

But on the torus, every point has a neighbourhood (obtained by removing two orthogonal circles from the torus) whose closure is the whole torus, and which is homeomorphic to the plane (can be "flattened" into a rectangle). That's what I mean. By saying that the neighbourhood is "Euclidean", I...

I meant a manifold that is connected (wrote it as "continuous" by accident). By "equals", i mean that the neighbourhood is dense in the manifold.

Does every (continous and second countable) topological manifold have an Euclidean neighbourhood around each of its points whose closure equals the whole manifold?