Geodesic
Topological properties of non-Archimedean approach spaces
Theory and applications of categories, Tome 32 (2017), pp. 1454-1484 Cet article a éte moissonné depuis la source Theory and Applications of Categories website

Voir la notice de l'article

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},
     year = {2017},
     volume = {32},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2017_32_a40/}
}
TY  - JOUR
AU  - Eva Colebunders
AU  - Karen Van Opdenbosch
TI  - Topological properties of non-Archimedean approach spaces
JO  - Theory and applications of categories
PY  - 2017
SP  - 1454
EP  - 1484
VL  - 32
UR  - http://geodesic.mathdoc.fr/item/TAC_2017_32_a40/
LA  - en
ID  - TAC_2017_32_a40
ER  - 
%0 Journal Article
%A Eva Colebunders
%A Karen Van Opdenbosch
%T Topological properties of non-Archimedean approach spaces
%J Theory and applications of categories
%D 2017
%P 1454-1484
%V 32
%U http://geodesic.mathdoc.fr/item/TAC_2017_32_a40/
%G en
%F TAC_2017_32_a40
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/