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In complex analysis, a complex domain (or simply domain) is any connected open subset of the complex plane C. For example, the entire complex plane is a domain, as is the open unit disk, the open upper half-plane, and so forth. Often, a complex domain serves as the domain of definition for a holomorphic function.
The term domain is also commonly used in a different sense in mathematical analysis: a domain is a non-empty connected open set in a topological space. In particular, in real and complex analysis , a domain is a non-empty connected open subset of the real coordinate space R n {\displaystyle \mathbb {R} ^{n}} or the complex coordinate space C n ...
An antonym is one of a pair of words with opposite meanings. Each word in the pair is the antithesis of the other. A word may have more than one antonym. There are three categories of antonyms identified by the nature of the relationship between the opposed meanings.
Atomic domain, an integral domain in which every nonzero non-unit is a finite product of irreducible elements; Bézout domain, an integral domain in which the sum of two principal ideals is again a principal ideal; Euclidean domain, an integral domain which allows a suitable generalization of the Euclidean algorithm
In algebra, a domain is a nonzero ring in which ab = 0 implies a = 0 or b = 0. [1] (Sometimes such a ring is said to "have the zero-product property".) Equivalently, a domain is a ring in which 0 is the only left zero divisor (or equivalently, the only right zero divisor). A commutative domain is called an integral domain.
[4] Roget's Thesaurus is composed of six primary classes. [5] Each class is composed of multiple divisions and then sections. This may be conceptualized as a tree containing over a thousand branches for individual "meaning clusters" or semantically linked words.
with domain, the range of , sometimes denoted or (), [4] may refer to the codomain or target set (i.e., the set into which all of the output of is constrained to fall), or to (), the image of the domain of under (i.e., the subset of consisting of all actual outputs of ). The image of a function is always a subset of the codomain of the ...
WordNet aims to cover most everyday words and does not include much domain-specific terminology. WordNet is the most commonly used computational lexicon of English for word-sense disambiguation (WSD), a task aimed at assigning the context-appropriate meanings (i.e. synset members) to words in a text. [ 14 ]