Word.ws English Dictionary

inverse limit

inverse limit noun: a subset of the Cartesian product of all the members of an inverse system, such that a member M of the subset is a sort of “cross section” of the inverse system (as fiber bundle) induced by the morphisms of it. (If i<j in the indexing poset then f_ij:A_j→A_i in the inverse system and if a_i∈A_i, a_j∈A_j are components of M then f_ij(a_j)=a_i).

Noun

inverse limit (plural inverse limits)

  1. A subset of the Cartesian product of all the members of an inverse system, such that a member M of the subset is a sort of “cross section” of the inverse system (as fiber bundle) induced by the morphisms of it. (If i<j in the indexing poset then f_ij:A_j→A_i in the inverse system and if a_i∈A_i, a_j∈A_j are components of M then f_ij(a_j)=a_i).
    • An inverse limit has “natural projections” which are restrictions of the projections of the Cartesian product (to a domain which is the inverse limit). The reason why the projections are described as “natural” would be the following: besides the functor from an index poset to the inverse system...
    • Inverse limits are concrete-categorical versions of limits.
  2. a limit

Synonyms of inverse limit

Antonyms

Forms of inverse limit

pluralinverse limits

Questions about inverse limit

What does inverse limit mean?
Inverse limit means a subset of the Cartesian product of all the members of an inverse system, such that a member M of the subset is a sort of “cross section” of the inverse system (as fiber bundle) induced by the morphisms of it. (If i<j in the indexing poset then f_ij:A_j→A_i in the inverse system and if a_i∈A_i, a_j∈A_j are components of M then f_ij(a_j)=a_i).
What part of speech is inverse limit?
Inverse limit is a noun.
What is the plural of inverse limit?
The plural of inverse limit is inverse limits.

Words near inverse limit in the dictionary

  1. inverse hyperbolic function
  2. inverse hyperbolic functions
  3. inverse image
  4. inverse images
  5. inverse kinematics
  6. inverse limit
  7. inverse limits
  8. inverse matrices
  9. inverse matrix
  10. inverse matrixes
  11. inverse number

Source and license

Adapted from Wiktionary: inverse limit (page history and authors). Text available under the Creative Commons Attribution-ShareAlike 4.0 license. Word.ws reformatted the entry and added links. Wiktionary data of 2026-09-02.

Last updated:

Cite this entry: “inverse limit.” Word.ws, https://word.ws/inverse_limit. Based on Wiktionary, CC BY-SA 4.0.