I provided the military definition above what a battle is.
It's like the liberals definition of an assault rifle. The worlds militaries have already defined what an assault rifle is, exactly what the Wehrmacht said it was. Most firearms that liberals have labeled as assault rifles only because they are scary looking to them are not considered to be assault rifles in any military.
To win a battle, territory has to be taken, occupied and held. Be it on land, sea or in the air.
The United States never attempted gaining air superiority over North Vietnam. But North Vietnam never had air superiority over their own country.