Title
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A finite axiom scheme for approach frames
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Author
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Abstract
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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. |
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Language
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English
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Source (journal)
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Bulletin of the Belgian Mathematical Society Simon Stevin. - Brussels, 1994, currens
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Publication
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Brussels
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2010
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ISSN
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1370-1444
[print]
2034-1970
[online]
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Volume/pages
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17
:5
(2010)
, p. 899-909
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