Mapping

The term mapping is often used synonymously with function, but also sometimes to indicate something more general, namely, a means of associating every object in a certain collection with a unique object in another collection, where these collections are not necessarily sets as defined in set theory.

In topology it is common to use mapping to mean "continuous function", in order to avoid overuse of the word "continuous".

The domain? of a mapping is the set of elements from which the mapping is valid, that is the set of valid starting points of a mapping.

Sometimes one refers to a [partial mapping]? being a mapping from a set where only a subset of the elements are part of the domain. A [total mapping]? from a set S is a mapping where S itself is the domain.

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