Like, for example, we could assume that it should be a space with discrete topology of some relevant cardinality. [...] Not sure what you mean by that, as each vote xi is generally not a function or a similar structure
Yeah that was badly written, sorry. I was taking the xi's as well-defined preference-based utility functions, so "i is xi important". That's not even continuous unless one could say "how much of our resources will be spent on i," which is a simplification itself. Maybe instead of issues having functions ki describing all possible choices regarding an issue? By limit I meant someone saying "i is infinitely important."
Anyway, I think it's possible to build a reasonable, continuous, preference model, depending on what the set of topics/issues looks like. Whether the properties required of the set of issues would be reasonable... I think not. I think one would end up with something maybe not discrete but certainly not continuous. Hence the second paragraph in my previous comment.
I've never heard of this. Just off the first sentence on Wikipedia, I'd question the existence of independent alternatives. It looks like non-dictatorship is defined to be ordering invariant?