Difference between revisions of "P Adic Solenoid"
(Created page with "The canonical group homomorphisms <center><cmath>\varphi_n:\mathbb{R}/p^{n+1}\mathbb{Z}\to \mathbb{R}/p^n\mathbb{Z},~x\pmod{p^{n+1}\mathbb{Z}}\mapsto x\pmod{p^n\mathbb{Z}}</cm...") |
(No difference)
|
Revision as of 15:04, 2 July 2022
The canonical group homomorphisms
![\[\varphi_n:\mathbb{R}/p^{n+1}\mathbb{Z}\to \mathbb{R}/p^n\mathbb{Z},~x\pmod{p^{n+1}\mathbb{Z}}\mapsto x\pmod{p^n\mathbb{Z}}\]](http://latex.artofproblemsolving.com/d/6/3/d63aef7196b69bcdc402968fc9be3f2a518ab6b0.png)
form a projective system 
of topological groups. The 
adic solenoid 
is a projective limit 
of the projective system . The Adic Solenoid is both compact and connected.
