Synonyms for Domain (same or very similar meaning)
WordNet sense 1 (a particular environment or walk of life):
area, arena, field, orbit, sphere
WordNet sense 2 (territory over which rule or control is exercised):
demesne, land
WordNet sense 3 (people in general; especially a distinctive group of people with some shared interest):
world
WordNet sense 4 (a knowledge domain that you are interested in or are communicating about):
realm, region
From the ODE community, based on WordNet
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