GENERAL TOPOLOGY on Distributive Set Theory
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Topology_on_DST_structurev1.v is a Coq library created by R. Dapoigny and P. Barlatier whose purpose is to propose a decidable and consistent structure of general topology . To reach that objective, the developed structure relies again on the Distributive Set Theory (DST for short) expressed in Dependent Type Theory and based on characteristic functions to formulate appropriate definitions. Then, using Clay’s single axiom for partial order, and adding the two basic axioms of general topology (i.e., union and intersection of open sets) we demonstrate that this axiom is provable assuming set inclusion as partial order and a universe of existing regular open sets. As a result, the developed library is a theoretical construct depending on few axioms and on a set of definitions.
- Coq (> v8.9)
- Click here to download Topology_on_DST_structure (7z file).
- Unzip the file content (e.g. with 7-zip) in your local directory.
- Start Coq.
- Open a new file and incorporate the external module “Topology_on_DST_structurev1.v” in order to use it.