@Ilya You probably know this already, but: I now think I showed $\tau_{prod} \subseteq \tau_D \subseteq \tau_{box}$. Do you agree with this?

Where showed means: I have to write down the last part of the proof (and it might turn out to be false).

Wrote down the last part.

It seems to be the case that $$ \tau_{prod} \subsetneq \tau_D \subsetneq \tau_{box}$$

If this is true it's cool : )

@MattN. I'm quite sure about the leftmost one

w.r.t. the rightmost - balls in $D$ are open in $\tau_{box}$?

@Ilya Yes I think I have a proof here for $\subseteq$. Let me type it (but first I must finish eating).

@MattN. enjoy :)

if you send it to me, I'll check it

@Ilya Ah, right, would you prefer latex/pdf via email? If so, sure thing, no problem.

@MattN. that would be nice - so that I can also edit something if needed

@Ilya In this case, would you be comfortable with using an online repository (such as github)? For convenient synchronisation.

@MattN. svn-like?

@Ilya Yes, with checkin/checkout on terminal.

Or is it overkill?

Hard to say how many edits each of us will be making.

@MattN. I'm using tortoise svn

but that's only for windows

Great. Then we could use unfuddle.com, I don't need Tortoise.

@MattN. so you tell me what shall I do, ok?

Yes. I'll send you an email once I texed it and set up a repository.

I'll see you later!

@MattN. sure, have fun