π-Base

a community database of topological counterexamples

➜ Search spaces by name/description: compactifications

➜ Search spaces by properties: non-metric continua

➜ Find counterexamples: connected spaces need not be path connected

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

Dedicated to the memory of our friend and mentor Gary Gruenhage (1947-2023).


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.

Community

The π-Base is part of the code4math community. Join the conversation on either the code4math Zulip or the π-Base GitHub Discussion board.

More databases may be discovered at the Index of Mathematical DataBases.

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: 2024-06-06).
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