π-Base: Topology

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 Steven Clontz joined the project in 2017.

In 2026, the π-Base project officially expanded to serve disciplines beyond topology.

Community

The topology π-Base would not be possible without the volunteer efforts of our numerous contributors.

The π-Base is part of the code4math community. Join the conversation on our code4math Zulip channel.

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 π-Base Community. π-Base Topology: a community database of topological counterexamples. Available at: http://sveltekit-prerender/ (Accessed: 2026-06-25).
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