- #1
Wodfrag
- 3
- 0
Homework Statement
If the set \Z of integers is equipped with the relative topology inherited from ℝ, and κ:\Z→\Z_n (where κ is a canonical map and \Z_n is the residue class modulo n) what topology/topologies on \Z_n will render κ globally continuous?
Homework Equations
The Attempt at a Solution
I think i have found that κ will be globally continuous if \Z_n is equipped with the trivial (where the open sets are ∅ and \Z_n itself) topology, since \Z_n itself will be an open neighborhood of an element in \Z_n, hence for every x \in \Z κ(x)\in \Z_n. I cannot figure out however if i can apply any other topologies on \Z_n such that κ will be globally continuous.
Thanks