Word Pronunciation & Dictionary

inverse limit

Word Rarity Rare

Frequency: Zipf frequency 3.40 in modern English

Syllables: in-verse lim-it
IPA

17

Scrabble Score

12

Letters

3

Syllables

9

Unique Chars

Meaning

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 iindexing 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

Example Sentences

"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, there is another functor from the same index poset to the inverse limit of that system, this functor being a constant functor. Then there is a natural transformation from the constant functor to the inverse limit’s functor: the components of such natural transformation are the said “natural projections”."
"Inverse limits are concrete-categorical versions of limits."

Inflected Forms

inverse limits (plural)

Phrases

inverse system

Frequently Paired Words

inverse system

Synonyms

projective limit

Antonyms

direct limit

Questions

What does inverse limit mean?: 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 iindexing 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).

How to pronounce inverse limit

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