View Single Post
Sci Advisor
P: 1,716

## Is R mod 2pi a Compact Manifold?

 Quote by Bahram_phd Hi, Why R mod 2pi is a Compact Manifold? Isn't this like a real line which is not compact? How should we prove it using a finite sub-cover for this manifold? bah
What is the topology that you want?
If it is R with the topology of a line modulo the discrete group of integer multiples of 2pi, then use the definition of open set in the quotient topology to show that every open cover has a finite subcover. You need to know that a closed interval is compact.