π-Base

a community database of topological counterexamples

➜ Search spaces by name/description: compactifications

➜ Search spaces by properties: non-metric continua

➜ Find counterexamples: first countable spaces need not be locally pseudometrizable

Topology is a dense forest of counterexamples. A usable map of the forest is a fine thing.

Paraphrased from Mary Ellen Rudin's review of Counterexamples in Topology

Contributing

π-Base's data and software are open-sourced on GitHub. We rely on volunteers like yourself to contribute new spaces, properties, and theorems.

About Us

The π-Base was founded in 2014 by its lead maintainer James Dabbs. π-Base's lead mathematical editor and contributing research software engineer Steven Clontz joined the project in 2017.

Other Mathematical Databases

Integer sequences: OEIS | L-functions and modular forms: LMFDB | Rings and modules: DaRT | Graphs: HoG

And many more: Catalogue of Mathematical Datasets

The π-Base software was designed to support any category of objects/properties/theorems. If you're interested in adapting π-Base for use in your field, reach out to us on GitHub.

Special Acknowledgements

Many people have contributed to this project, but a few individuals and organizations deserve particular recognition:

Cite as: The pi-Base Community. π-Base, a community database of topological counterexamples. Available at: (Accessed: 2023-12-06).
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