Airspace is the sky over a country that the country treats as its own, the way the land inside a border is its land. Planes need permission to fly through another country's airspace; if they do not have it, governments talk of a violation, not just a flying mistake. News uses close airspace, enter airspace, restrict airspace — often in wars, protests, or when a volcano fills the sky with ash. It is a formal, news-and-aviation word; you would not use it for the sky above your house unless you were joking. Though actually, pilots and air-traffic people also use airspace for a slice of sky that is not a whole country: a city's airspace, military airspace, controlled airspace — meaning a volume of sky with rules. The learner-dictionary picture is the country one; real talk is a bit wider. Still, the legal “this sky belongs to this country” sense is the one you will meet first in newspapers.