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Synthetic Topology and Constructive Metric Spaces
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The thesis presents the subject of synthetic topology, especially with relation to metric spaces. A model of synthetic topology is a categorical model in which objects possess an intrinsic topology in a suitable sense, and all morphisms are continuous with regard to it. We redefine synthetic topology in order to incorporate closed sets, and several generalizations are made. Real numbers are reconstructed (to suit the new background) as open Dedekind cuts. An extensive theory is developed when metric and intrinsic topology match. In the end the results are examined in four specific models.
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Cited by 1 Pith paper
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A Foundation for Synthetic Stone Duality
Four new axioms for homotopy type theory, modeling light condensed sets, suffice to develop synthetic topology and prove Brouwer's fixed-point theorem, with all functions continuous on the interval.
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