A topological space G is called a topological group if G forms a group under an...

Transcribed Image Text:

A topological space G is called a topological group if G forms a group under an operation such that (g, h)g.h, Vg, h E G and g+g, Vg G are continuous maps. Let G be a topological group and let H be a subgroup of G. (a) Show that the quotient map G G/H is an open map. (b) Show that if HG, then G/H is a topological group. (c) Show that R/Z is a topological group. Describe this group. A topological space G is called a topological group if G forms a group under an operation such that (g, h)g.h, Vg, h E G and g+g, Vg G are continuous maps. Let G be a topological group and let H be a subgroup of G. (a) Show that the quotient map G G/H is an open map. (b) Show that if HG, then G/H is a topological group. (c) Show that R/Z is a topological group. Describe this group.

Answer rating: 100% (QA)

The detailed ... View the full answer