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Welcome to the π-Base

A community database of topological examples with automated deduction and powerful search

The instructions below assume you have javascript enabled, but it appears you do not.

If you can't (or don't want to) enable javascript, you will need to enclose ands and ors with quotations, and use { "property_id": true/false } in place of property names.

For example, you would specify Compact (id 16), Connected (id 36), non-Metrizable spaces with

 {"and": [ {"16": true}, {"36": true}, {"53": false} ] }


Use ~ for negation and {and: [...]} or {or: [...]} for nested formuale.

You may enable different search modes by starting your query with certain special characters

  • : - spaces by name
  • ? - spaces where formula is indeterminate
  • ! - spaces where formula is disprovable

Note that properties containing spaces or special characters may need to be enclosed in quotations.


All Non-Metric Continua
 {and: [compact, connected, t_2, ~metrizable]}
A Common Non-Theorem
 {and: ["first countable", separable, "~second countable"]}
A Class of Examples by Name
New Things to Prove