# Every continuous map from a non-empty connected space to a discrete space is constant

## Statement

Let [ilmath](X,\mathcal{ J })[/ilmath] be a non-empty[Note 1] connected topological space and let [ilmath](Y,\mathcal{P}(Y))[/ilmath] be any discrete topological space, then[1]:

## Proof

This page requires one or more proofs to be filled in, it is on a to-do list for being expanded with them.
Please note that this does not mean the content is unreliable. Unless there are any caveats mentioned below the statement comes from a reliable source. As always, Warnings and limitations will be clearly shown and possibly highlighted if very important (see template:Caution et al).
The message provided is:
Easy proof to do, I've done it on paper and there is nothing nasty about it

This proof has been marked as an page requiring an easy proof