Details
| Original language | English |
|---|---|
| Pages (from-to) | 103-125 |
| Number of pages | 23 |
| Journal | Annals of the New York Academy of Sciences |
| Volume | 704 |
| Issue number | 1 |
| Publication status | Published - 17 Dec 2006 |
Abstract
ABSTRACT. The rudiments of the theory of Galois connections (or residuation theory, as it is sometimes called) are provided, together with many examples and applications. Galois connections occur in profusion and are well known to most mathematicians who deal with order theory; they seem to be less known to topologists. However, because of their ubiquity and simplicity, they (like equivalence relations) can be used as an effective research tool throughout mathematics and related areas. If one recognizes that a Galois connection is involved in a phenomenon that may be relatively complex, then many aspects of that phenomenon immediately become clear, and thus, the whole situation typically becomes much easier to understand.
Keywords
- axiality, closure operation, Galois connection, interior operation, polarity
ASJC Scopus subject areas
- Neuroscience(all)
- General Neuroscience
- Biochemistry, Genetics and Molecular Biology(all)
- General Biochemistry,Genetics and Molecular Biology
- Arts and Humanities(all)
- History and Philosophy of Science
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In: Annals of the New York Academy of Sciences, Vol. 704, No. 1, 17.12.2006, p. 103-125.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - A Primer on Galois Connections
AU - ERNÉ, M.
AU - STRECKER, G. E.
AU - Koslowski, Jürgen
AU - Melton, Austin
PY - 2006/12/17
Y1 - 2006/12/17
N2 - ABSTRACT. The rudiments of the theory of Galois connections (or residuation theory, as it is sometimes called) are provided, together with many examples and applications. Galois connections occur in profusion and are well known to most mathematicians who deal with order theory; they seem to be less known to topologists. However, because of their ubiquity and simplicity, they (like equivalence relations) can be used as an effective research tool throughout mathematics and related areas. If one recognizes that a Galois connection is involved in a phenomenon that may be relatively complex, then many aspects of that phenomenon immediately become clear, and thus, the whole situation typically becomes much easier to understand.
AB - ABSTRACT. The rudiments of the theory of Galois connections (or residuation theory, as it is sometimes called) are provided, together with many examples and applications. Galois connections occur in profusion and are well known to most mathematicians who deal with order theory; they seem to be less known to topologists. However, because of their ubiquity and simplicity, they (like equivalence relations) can be used as an effective research tool throughout mathematics and related areas. If one recognizes that a Galois connection is involved in a phenomenon that may be relatively complex, then many aspects of that phenomenon immediately become clear, and thus, the whole situation typically becomes much easier to understand.
KW - axiality
KW - closure operation
KW - Galois connection
KW - interior operation
KW - polarity
UR - http://www.scopus.com/inward/record.url?scp=0027892934&partnerID=8YFLogxK
U2 - 10.1111/j.1749-6632.1993.tb52513.x
DO - 10.1111/j.1749-6632.1993.tb52513.x
M3 - Article
AN - SCOPUS:0027892934
VL - 704
SP - 103
EP - 125
JO - Annals of the New York Academy of Sciences
JF - Annals of the New York Academy of Sciences
SN - 0077-8923
IS - 1
ER -