galois connection
Word Rarity
Very rare
Frequency: Zipf frequency 2.15 in modern English
21
Scrabble Score
16
Letters
5
Syllables
10
Unique Chars
Meaning
noun
A type of correspondence between partially ordered sets (posets), also applicable to preordered sets.
Example Sentences
- "1986, Horst Herrlich, Miroslav Hušek, Galois Connections, Austin Melton, Mathematical Foundation of Programming Semantics: International Conference, Proceedings, Springer, Lecture Notes in Computer Science: 239, page 122, Define maps G:A→B and F:B→A by G(a)=y!∈!Y|∀x!∈!axρy and F(b)=x!∈!X|∀y!∈!bxρy. Then (F,G) is called a Galois connection of the first kind."
- "Finally, we discuss Galois connections. It is interesting to note that these definitions can be found in Birkhoff (1940, 1948, 1967) under the heading of "polarities," and Everett (1944) showed that all Galois connections defined on power sets can be obtained from polarities."
- "Galois connections appear in several areas of mathematics and computer science, and their applications. A Galois connection between sets X and Y is a pair #92;left#92;langle#92;uparrow,#92;downarrow#92;right#92;rangle of mappings #92;uparrow assigning subcollections of Y to subcollections of X, and #92;downarrow assigning subcollections of X to subcollections of Y."
Etymology
From Galois (attributive form of Galois theory) + connection; ultimately after French mathematician Évariste Galois. Coined by Norwegian mathematician Øystein Ore in 1944, Galois connexions, Transactions of the American Mathematical Society, 55, pages 493-513.
Inflected Forms
Galois connections (plural)
Galois connexion (alternative)