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.
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