/sci/ - Science & Math

>>11265160
I'm aware that, I think, the topology of any topological vector space over R can be consdier to be generated by its balls.
So let's think of e.g. algebraic topology over a finite field where this is out of the question by the Zariski topology still exist:

I'm in search for a tool or theorem from plain* topology (only proven from the fact that we have a notion of open sets here and so on, not dependent on us working e.g. with coordinate rings and their arithmetic operations) being used in a context of a topology T that is not induced by a metric.

*plain as in Tychonoff's theorem, which is really only dependent on the theory of topology