A finite axiom scheme for approach framesA finite axiom scheme for approach frames
Faculty of Sciences. Mathematics and Computer Science

Faculty of Design Sciences

Analytical and topological structures

Fundamental Mathematics

article

2010Brussels, 2010

Engineering sciences. Technology

Bulletin of the Belgian Mathematical Society Simon Stevin. - Brussels, 1994, currens

17(2010):5, p. 899-909

1370-1444

E

English (eng)

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.