Timeline for Two Definitions of "Character" of topological groups
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 19, 2012 at 23:25 | vote | accept | Hiro | ||
| Jan 19, 2012 at 23:25 | comment | added | Hiro | I found a way to show surjectivity... Let f:G->T be a character. The torus T has an open neighborhood U of 0 s.t. U contains no subgroup of T except for {0}. Take an open subgroup H of G contained in the inverse image of U. Then, H is contained in the kernel of the character f. So, f factors through the finite group G/H... Thanks for your advice! | |
| Jan 19, 2012 at 21:36 | comment | added | Hiro | Thank you for your advice. I could prove that the first functor Hom(-,Q/Z) has such property, but I have difficulty in proving the statement for the latter functor Hom(-,R/Z). I could show that the natural map colim(Hom(G_i,R/Z)) -> Hom(lim(G_i),R/Z) is injective, but cannot show that it is surjective. Will you please tell me how to do it? | |
| Jan 19, 2012 at 11:47 | history | answered | Xandi Tuni | CC BY-SA 3.0 |