Real Dictionary

arena
countable noun: An arena is a place where sports, entertainments, and other public events take place. It has seats around it where people sit and watch.
countable noun: You can refer to a field of activity, especially one where there is a lot of conflict or action, as an arena of a particular kind.

arena in American English
the central part of an ancient Roman amphitheater, where gladiatorial contests and shows took place
noun: the oval space in the center of a Roman amphitheater for gladiatorial combats or other performances

arena in British English
noun: an enclosure or platform, usually surrounded by seats on all sides, in which sports events, contests, entertainments, etc, take place