connected manifolds with infinite or n charts

Question

does anybody know that there exists a manifold which has an infinite chart for cover it or not? My teacher and I could not find.

I have tried it but all the manifolds I know are covering with two or 3 charts.

Edit: I thought sphere with n-dimensional which cut with a KNOT and torus should have more than 3 charts.

Answer 1

Quotes from Mathoverflow (Least number of charts to describe a given manifold):

The question:

I'm wondering if there is a standard reference discussing the least number of charts in an atlas of a given manifold required to describe it.

One answer:

I have found on the second page of Michor "Topics in Differential Geometry": "Note finally that any manifold $M$ admits a finite atlas consisting of $\dim M + 1$ not connected charts. This is a consequence of topological dimension theory [cf. Nagata, Modern Dimension Theory]; a proof for manifolds may be found in [cf. Greub, Halperin, Vanstone, Connections, curvature and cohomology. I]."

The charts can be disconnected. Is this OK?