I captured a gym today just before the servers went down. I am wondering if I lost my progress. Is there a way to see if I own a gym or not?
As of today, there is finally a way to see what gyms you have Pokémon occupying!
If you go to your trainer profile after visiting gyms, there will be a list of gym badges you've earned. There is an indicator next to the gyms that currently have one of your Pokémon occupying it:
If you tap on this gym badge, it will show what Pokémon you have defending that gym as well as how long that Pokémon has been defending the gym for.
If you keep personal track of which Pokemon you left where, then yes. The game shows a colored icon above one of your Pokemon if it's at a gym, but not which gym it is. You could also monitor which Pokemon you have at 1hp. Additionally, the icon in the top-right of the Shop (which you use to claim rewards for holding gyms) tells you the number of gyms you control.