Ontology type: schema:ScholarlyArticle Open Access: True
2017-12
AUTHORSJ. Bruno, P. Szeptycki
ABSTRACTPremetrics and premetrisable spaces have been long studied and their topological interrelationships are well-understood. Consider the category Pre of premetric spaces and š ā Ī“ continuous functions as morphisms. The absence of the triangle inequality implies that the faithful functor PreāTop - where a premetric space is sent to the topological space it generates - is not full. Moreover, the sequential nature of topological spaces generated from objects in Pre indicates that this functor is not surjective on objects either. Developed from work by Flagg and Weiss, we illustrate an extension PreāŖP together with a faithful and surjective on objects left adjoint functor PāTop as an extension of PreāTop. We show this represents an optimal scenario given that PreāTop preserves coproducts only. The objects in P are metric-like objects valued on value distributive lattices whose limits and colimits we show to be generated by free locales on discrete sets. More... »
PAGES1045-1058
http://scigraph.springernature.com/pub.10.1007/s10485-016-9465-8
DOIhttp://dx.doi.org/10.1007/s10485-016-9465-8
DIMENSIONShttps://app.dimensions.ai/details/publication/pub.1024304879
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