Cartesian closed hull for (quasi-)metric spaces (revisited)
Nauwelaerts, Mark
Commentationes Mathematicae Universitatis Carolinae, Tome 41 (2000), p. 559-573 / Harvested from Czech Digital Mathematics Library
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An existing description of the cartesian closed topological hull of $p\text{\bf MET}^\infty$, the category of extended pseudo-metric spaces and nonexpansive maps, is simplified, and as a result, this hull is shown to be a special instance of a ``family'' of cartesian closed topological subconstructs of $pqs\text{\bf MET}^\infty$, the category of extended pseudo-quasi-semi-metric spaces (also known as quasi-distance spaces) and nonexpansive maps. Furthermore, another special instance of this family yields the cartesian closed topological hull of $pq\text{\bf MET}^\infty$, the category of extended pseudo-quasi-metric spaces and nonexpansive maps (which has recently gained interest in theoretical computer science), and this hull is also shown to be a nice generalization of $\text{\bf Prost}$, the category of preordered spaces and relation preserving maps.

Publié le : 2000-01-01
Classification:  18B99,  18D15,  54C35,  54E99 
@article{119189,
     author = {Mark Nauwelaerts},
     title = {Cartesian closed hull for (quasi-)metric spaces (revisited)},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     volume = {41},
     year = {2000},
     pages = {559-573},
     zbl = {1034.18008},
     mrnumber = {1795085},
     language = {en},
     url = {http://dml.mathdoc.fr/item/119189}
}

Nauwelaerts, Mark. Cartesian closed hull for (quasi-)metric spaces (revisited). Commentationes Mathematicae Universitatis Carolinae, Tome 41 (2000) pp. 559-573. http://gdmltest.u-ga.fr/item/119189/

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