## A Primer On Galois Connections (1992)

Venue: | York Academy of Science |

Citations: | 29 - 3 self |

### BibTeX

@INPROCEEDINGS{Erne92aprimer,

author = {M. Erne and J. Koslowski and A. Melton and G.E. Strecker},

title = {A Primer On Galois Connections},

booktitle = {York Academy of Science},

year = {1992}

}

### Years of Citing Articles

### OpenURL

### Abstract

: We provide the rudiments of the theory of Galois connections (or residuation theory, as it is sometimes called) 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. KEY WORDS: Galois connection, closure operation, interior operation, polarity, axiality CLASSIFICATION: Primary: 06A15, 06--01, 06A06 Secondary: 54-01, 54B99, 54H99, 68F05 0. INTRODUCTION Mathematicians are familiar with the following situation: there are two "worlds" and t...