environment vs arena

environment and arena both are nouns.

Word	Noun	Adjective	Verb	Adverb
environment	Yes	No	No	No
arena	Yes	No	No	No

As nouns, arena is a hyponym of environment; that is, arena is a word with a more specific, narrower meaning than environment:

environment (noun)	arena (noun)
the area in which something exists or lives	a playing field where sports events take place
the totality of surrounding conditions	a large structure for open-air sports or entertainments
	the central area of an ancient Roman amphitheater where contests and spectacles were held; especially an area that was strewn with sand
	a particular environment or walk of life