Some of the things I've learned every day since Oct 10, 2016
Category Archives: topology
January 23, 2017Posted by on
The Möbius strip is a canonical and minimal example of a non-orientable surface, in the sense that
- a surface is non-orientable if and only if it has the Möbius strip as a topological subspace, and
- the Möbius strip is the only surface with this property.
December 11, 2016Posted by on
Given any division of a (2-)torus into regions, it is possible to color the regions with 7 distinct colors so that no two adjacent regions have the same color.
This contrasts with the more well-known fact that the plane is 4-colorable.