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The quasitopos hull of the construct of closure spaces

Authors: Claes, Veerle; Sonck, Gert;

The quasitopos hull of the construct of closure spaces

Abstract

<p>In the list of convenience properties for topological constructs the property of being a quasitopos is one of the most interesting ones for investigations in function spaces, differential calculus, functional analysis, homotopy theory, etc. The topological construct Cls of closure spaces and continuous maps is not a quasitopos. In this article we give an explicit description of the quasitopos topological hull of Cls using a method of F. Schwarz: we first describe the extensional topological hull of Cls and of this hull we construct the cartesian closed topological hull.</p>

Countries
Belgium, Spain
Keywords

quasitopos, QA299.6-433, extensional topological construct, Topoi, Cartesian closed topological hull, Topological construct, topological construct, Extensional topological construct, Categories of topological spaces and continuous mappings, Cartesian closed category, Quasitopos, Closure space, closure space, Function spaces in general topology, cartesian closed category, QA1-939, Closed categories (closed monoidal and Cartesian closed categories, etc.), Topological spaces and generalizations (closure spaces, etc.), Categories admitting limits (complete categories), functors preserving limits, completions, cartesian closed topological hull, Mathematics, Analysis

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selected citations
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This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
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