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 subcover 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.