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<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>
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
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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