We aim to create a database of theorems and counterexamples in point-set topology. The starting point for this project is "Counterexamples in Topology" by Steen and Seebach.
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 Failed to load latest commit information. README cardinality-theorems.txt compactness-theorems.txt connectedness-theorems.txt counterexamples.txt metric-space-theorems.txt separation-theorems.txt topological-properties.txt topology.htm

Hausdorff project
=================

The goal of this project is to create a database and a set of tools for exploring theorems
and counterexamples in Topology. The starting point is the classic book "Counterexamples in
Topology" by Lynn Steen and J. Arthur Seebach.

DATA FILES
==========

topological-properties.txt

A text file listing the topological properties in Steen and Seebach.
The properties are numbered from 1 to 61.
The first column contains a number from 1 to 61, and the second column
contains the name of the property.
The columns are separated by a single tab character.

counterexamples.txt

This file contains the tables from an appendix of Steen and Seebach.
The columns are separated by tabs.
The first column is the ID number of the counterexample from the text.
The second column is the name of the counterexample.
Columns 3-63 are the topological properties from the previous file.
The entries in columns 3-63 are integers between 0 and 3 inclusive.
0 = The space does not have the indicated property.
1 = The space has the indicated property.
2 = It is unknown whether the space has the indicated property.
3 = The property is not applicable, or it depends.

compactness-theorems.txt

A list of logical dependencies related to compactness properties.
Each theorem is a disjunction of the topological properties and their negations.
Properties are indicated by their code numbers (1-61).
Negations of properties are indicated by negative numbers.
Each theorem is on a separate line beginning with @.

Example: "Compact (16) implies Sigma-compact (17)" is written as "@ -16 17".

Lines that do not begin with @ are comments for human readers.

connectedness-theorems.txt
metric-space-theorems.txt
separation-theorems.txt

These files contain other lists of theorems, in the format described above.