Etymology
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domain (n.)

c. 1600, "territory over which dominion is exerted," from French domaine "domain, estate," from Medieval Latin domanium "domain, estate," from Latin dominium "property, dominion," from dominus "lord, master, owner," from domus "house" (from PIE root *dem- "house, household"). A later borrowing from French of the word which became demesne.

Sense of "dominion, province of action" is from 1727. Meaning "range or limits of any department of knowledge or sphere of action" is from 1764. Internet domain name is attested by 1985. Via the notion of "ownership of land" comes legal eminent domain "ultimate or supreme lordship over all property in the state" is attested from 1738.

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Definitions of domain

domain (n.)
a particular environment or walk of life;
Synonyms: sphere / area / orbit / field / arena
domain (n.)
territory over which rule or control is exercised;
his domain extended into Europe
Synonyms: demesne / land
domain (n.)
(mathematics) the set of values of the independent variable for which a function is defined;
Synonyms: domain of a function
domain (n.)
people in general; especially a distinctive group of people with some shared interest;
Synonyms: world
domain (n.)
the content of a particular field of knowledge;
Synonyms: knowledge domain / knowledge base
From wordnet.princeton.edu