Geodesic
Topological properties of non-Archimedean approach spaces
Theory and applications of categories, Tome 32 (2017), pp. 1454-1484

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In this paper we give an isomorphic description of the category of non-Archimedian approach spaces as a category of lax algebras for the ultrafilter monad and an appropriate quantale. Non-Archimedean approach spaces are characterised as those approach spaces having a tower consisting of topologies. We study topological properties p, for p compactness and Hausdorff separation along with low-separation properties, regularity, normality and extremal disconnectedness and link these properties to the condition that all or some of the level topologies in the tower have p. A compactification technique is developed based on Shanin's method.

Publié le :
Classification : 18C15, 18C20, 54A05, 54B30, 54E99
Keywords: Lax algebra, quantale, non-Archimedean approach space, quasi-ultrametric space, initially dense object, topological properties in $(\beta, P_\wedge$-Cat, compactification 
@article{TAC_2017_32_a40,
     author = {Eva Colebunders and Karen Van Opdenbosch},
     title = {Topological properties of {non-Archimedean} approach spaces},
     journal = {Theory and applications of categories},
     pages = {1454--1484},
     publisher = {mathdoc},
     volume = {32},
     year = {2017},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2017_32_a40/}
}
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Eva Colebunders; Karen Van Opdenbosch. Topological properties of non-Archimedean approach spaces. Theory and applications of categories, Tome 32 (2017), pp. 1454-1484. http://geodesic.mathdoc.fr/item/TAC_2017_32_a40/