Contribution: Topology

General Topology

Authors

• Daniel Schepler

Description

This library develops some of the basic concepts and results of general topology.

Keywords

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

Topology Coq contribution

This library is free software; you can redistribute it and/or
modify it under the terms of the GNU Lesser General Public
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

```