@Ilya Are you still planning to ask a question about $\mathbb R^{\mathbb N}$? Because I am interested in asking whether there are other topologies in between.

@MattN.: yes, in a couple of weeks perhaps. Would it be possible for you to be that patient? ^_^

I guess there are infinitely many of them, but it would be interesting to know whether there are some cool ones. Also, I wonder about the topology induced by the Hausdorff distance

@Ilya Yes of course. But let's make sure not to forget about it. ^^

@MattN. I won't, gonna do research on a topic where it is used - just buy with other stuff now. I'll let you know