Title
A finite axiom scheme for approach frames A finite axiom scheme for approach frames
Author
Faculty/Department
Faculty of Sciences. Mathematics and Computer Science
Faculty of Design Sciences
Publication type
article
Publication
Brussels ,
Subject
Engineering sciences. Technology
Source (journal)
Bulletin of the Belgian Mathematical Society Simon Stevin. - Brussels, 1994, currens
Volume/pages
17(2010) :5 , p. 899-909
ISSN
1370-1444
Carrier
E
Target language
English (eng)
Abstract
The theory of approach spaces has set the context in which numerical topological concepts exist. The successful interaction between frames and topology on the one hand and the search for a good notion of sobriety in the context of approach theory on the other hand was the motivation to develop a theory of approach frames. The original definition of approach frames was given in terms of an implicitly defined set of equations. In this work, we describe a subset of this by a finite axiom scheme (of only six types of equations) which implies all the equations originally involved and hence provides a substantial simplification of the definition of approach frames. Furthermore we show that the category of approach frames is the Eilenberg-Moore category for the monad determined by the functor which takes each approach frame to the set of its regular functions.