If you win the hyperspace or show of force, can you build on it after. I believe so but wanted to confirm, if no where in the book does it specify?

Yes.

All you need to do, is win a Battle, to be eligible to build an outpost or base.

3 minutes ago, Drasnighta said:

Yes.

All you need to do, is win a Battle, to be eligible to build an outpost or base.

I assume that once you're out of bases and outposts, you don't get the planet's resources (therefore the empire is limited to 6(?) bases and the rebels to 12 outposts/bases, and thus planets)?

4 minutes ago, GhostofNobodyInParticular said:

I assume that once you're out of bases and outposts, you don't get the planet's resources (therefore the empire is limited to 6(?) bases and the rebels to 12 outposts/bases, and thus planets)?

Winning a battle is but one piece of the eligability critera.

Having a base available is another.

Having the resources to build it is another.

You only generate Resource income, specifically from Planets with Bases/Outposts, and the Special missions where appropriate.

If you're already maxed out, and you win... Too bad. NoSoupForYou!

Also, the Base Destruction and Base Building are at two separate times, with Destruction happening first.

So say the Rebels assault Corfai and Win, Destroying an Empire Base - The Empire player who won at Talfalgio can "rebuild" a base there, if he decides to spend the resources.