Spaces modelled by an algebra on [0,<tex>$\infty$</tex>] and their complete objects
Spaces modelled by an algebra on [0,<tex>$\infty$</tex>] and their complete objects
Faculty of Sciences. Mathematics and Computer Science

article

2010
Amsterdam
, 2010

Mathematics

Topology and its applications. - Amsterdam

157(2010)
:8
, p. 1335-1346

0166-8641

000277677500008

E

English (eng)

University of Antwerp

We study constructs of type View the MathML source consisting of affine sets over [0,∞] modelled by some algebra Ω. The categorical theory of closure operators is used to study separated and complete objects with respect to the Zariski closure operator, naturally defined in any category View the MathML source. Several basic examples are provided, in particular we show that the construct of approach spaces, the constructs of pseudo (quasi) metric spaces with contractions, the construct of topological spaces and several of its subconstructs and the construct of non-Archimedean spaces all fit into this setting.

https://repository.uantwerpen.be/docman/iruaauth/d14591/acf998fb477.pdf

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