inverse limit

The 'inverse limit' is a fundamental concept in mathematics used to combine a sequence of objects and morphisms into a single, coherent object, capturing the structure of the entire sequence.

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Definition

C2Category Theory

(technical, academic)A construction that combines a sequence of objects and morphisms in a way that reflects the structure of the entire sequence.

Example

  • The inverse limit allows us to study the properties of the entire sequence through a single object.

C2Topology

(technical, academic)A space formed as the limit of a sequence of topological spaces and continuous maps, encapsulating the information of the entire sequence.

Example

  • The inverse limit of these topological spaces provides a new space that retains the properties of each space in the sequence.

C2Algebra

(technical, academic)A set consisting of sequences of elements from a series of sets that are compatible with given functions, representing the limiting behavior of the sequence.

Example

  • The inverse limit in algebra can help in understanding the behavior of sequences of algebraic structures.

Similar

Terms that have similar or relatively close meanings to "inverse limit":

direct limitfixed limitlimit bidleft inversequantum limittime limitterm limit