Local (mathematics)

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In mathematics, local generally means that a property or behaviour at a point depends only on that point, or one points close to it. Often, it means locally determined -- some global property is determined completely by the way things behave locally. In addition to local being used as an adjective, locally is also used as an adverb, typically as a modifier to existing properties to indicate that these properties are only satisfied locally.

In ring theory

In both commutative and noncommutative algebra:

Local ring

Local field

In topology

Locally compact space

Locally connected space

Locally path-connected space

In group theory

Local subgroup: A subgroup of a group that occurs as the normalizer of a nontrivial solvable subgroup.

Primary subject wiki entry: Groupprops:Local subgroup