> Moreover, you can do different things with them such as create homeomorphisms to another topology much more easily than you can create bijections between graphs. In general, continuity lets you assume things that are impossible in discrete spaces.
If you argue with more generality: why not consider sites (and, relatedly, topoi) instead of topological spaces then:
> If you argue with more generality: why not consider sites (and, relatedly, topoi) instead of topological spaces then:
I thought linear programming would be something everyone knows, and I am not the original author so I can't speak for why they chose topological spaces instead of anything listed here. I think their e-mails are on the paper. Perhaps e-mailing them will help elucidate their choice.
If you argue with more generality: why not consider sites (and, relatedly, topoi) instead of topological spaces then:
> https://en.wikipedia.org/wiki/Grothendieck_topology
> https://en.wikipedia.org/wiki/Topos