23,956 reputation
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bio website pdmi.ras.ru/~svivanov
location Saint Petersburg, Russia
age 42
visits member for 4 years, 9 months
seen Dec 12 at 20:13
I am a research fellow at St.Petersburg Department of Steklov Math Institute

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Feb
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answered Is a left topological group which is a manifold a topological group?
Feb
17
comment Characterization of discs
There are still counter-examples with the formulation "open set homeomorphic to the disc". For example, start with the unit disc and remove a segment between a point in the boundary and a point inside. You can then remove a small disc centered at the interior endpoint, and so on. In these examples, the boundary contains the unit circle so the property holds as stated. You need to assume that there are no other points on $L\cap\partial D$.
Feb
17
comment A Converse to the Gauss Bonnet Theorem
For example, contract a hemisphere to a segment by contracting each radial circle to a point. The resulting space is a bouquet of a sphere and a circle. Place the segment to the sphere by an injective map. This can be made smooth.
Feb
14
comment A Converse to the Gauss Bonnet Theorem
Take a point with the highest $z$-coordinate. If it is on the boundary, take one with the lowest $z$-coordinate. Since the entire boundary is on the same level, either a highest or lowest point is in the interior.
Feb
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answered A Converse to the Gauss Bonnet Theorem
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