Synthetic Topology and Constructive Metric Spaces
Davorin Le\v{s}nik

TL;DR
This thesis explores synthetic topology within metric spaces, redefining the framework to include closed sets, reconstructing real numbers, and analyzing models where metric and intrinsic topologies align.
Contribution
It introduces a revised synthetic topology model incorporating closed sets and reconstructs real numbers as open Dedekind cuts, expanding the theoretical foundation.
Findings
Redefinition of synthetic topology to include closed sets
Reconstruction of real numbers as open Dedekind cuts
Analysis of models where metric and intrinsic topologies match
Abstract
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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsConstraint Satisfaction and Optimization · Advanced Algebra and Logic · Rough Sets and Fuzzy Logic
