Indexets

Indexets is a term that appears in several languages and disciplines but is not a standard term in English-language mathematics. In Scandinavian languages, such as Swedish, indexet means "the index" and indexets can be the definite or possessive form used in phrases. In English-language texts, the closest conventional term is "index set" or "indexing set."

In mathematics, an index set I is used to label members of a family of objects {a_i}. The index set keeps track of which object is which. For example, a sequence (a_n) is a family indexed by the natural numbers N. A more general construction is a family (a_i)_{i in I}.

Index sets appear in analysis and topology; nets use directed index sets to generalize sequences. Families of functions, measures, or topologies may be indexed by I. The index set thus plays the role of an indexing parameter that organizes an entire collection.

In information retrieval and databases, the term index refers to a data structure that allows fast lookup; the collection of keys or positions used to locate records can be described as an index set, though more common language is "index keys" or "index entries."

Because "indexets" is not a standardized term in English, its precise meaning is determined by context. When writing about mathematics, it is safer to use "index set" or "indexing family" to avoid ambiguity.