- Daniel Schepler
This library develops some of the basic concepts and results of general topology.
topology, filters, nets, metric spaces, real analysis, urysohn's lemma, tietze extension theorem
This library develops some of the basic concepts and results of general topology. The library depends on my ZornsLemma contribution. The provided makefile expects compiled files to be present in ../ZornsLemma; if you have them somewhere else, first run coq_makefile -R /path/to/ZornsLemma ZornsLemma -R . Topology *.v > makefile before running make. Contents, roughly grouped in related categories: Basic definitions: TopologicalSpaces.v InteriorsClosures.v Neighborhoods.v OpenBases.v NeighborhoodBases.v Subbases.v Continuity.v Homeomorphisms.v Filters and nets: Filters.v FilterLimits.v DirectedSets.v Nets.v FiltersAndNets.v - various transformations between filters and nets Properties: Compactness.v Connectedness.v CountabilityAxioms.v - first countable, second countable, separable, Lindelof SeparatednessAxioms.v - T0, T1, Hausdorff, etc. General constructions of topologies: OrderTopology.v StrongTopology.v - strong topology induced by a family of maps from topological spaces WeakTopology.v - weak topology induced by a family of maps to topological spaces ProductTopology.v SubspaceTopology.v ContinuousFactorization.v - a continuous map factors through its image Metric spaces: MetricSpaces.v Completeness.v Completion.v UniformTopology.v - the topology of uniform convergence Real analysis: SupInf.v RationalsInReals.v RTopology.v - definition and properties of topology on R RFuncContinuity.v - reproof of continuity of basic functions on R "First nontrivial results of topology": UrysohnsLemma.v TietzeExtension.v Author: Daniel Schepler Copyright: Topology Coq contribution Copyright (C) 2011 Daniel Schepler This library is free software; you can redistribute it and/or modify it under the terms of the GNU Lesser General Public License as published by the Free Software Foundation; either version 2.1 of the License, or (at your option) any later version. This library is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more details. You should have received a copy of the GNU Lesser General Public License along with this library; if not, write to the Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA