# Talk:Continuous map

## Claim

I noted:

UNPROVED: I suspect that this is the same as [ilmath]\forall\mathcal{O}\in\mathcal{K}[f(x_0)\in\mathcal{O}\implies f^{-1}(\mathcal{O})\in\mathcal{J}\wedge x_0\in f^{-1}(\mathcal{O})][/ilmath] - this is basically the same just on open sets instead

TODO: Investigate and prove the highlighted claim

(Leave any notes to self here)

It'd be good to have something on this somewhere. Also Boris confirmed this is indeed to strong. Somewhere... Alec (talk) 12:21, 11 May 2016 (UTC)