# Strongly rigid countable Hausdorff spaces

- Speaker(s)
**Taras Banakh**- Affiliation
- Ivan Franko National University of Lviv and UJK Kielce
- Date
- Jan. 24, 2024, 4:15 p.m.
- Information about the event
- Zoom
- Seminar
- Topology and Set Theory Seminar

A topological space $X$ is strongly rigid if every no-identity continuous self-map of $X$ is constant. Among known examples of strongly rigid spaces one can recall the famous Cook continua. In fact, every strongly rigid topological space is connected.

We shall explain how to construct strongly rigid COUNTABLE Hausdorff spaces.

Such countable Hausdorff spaces are connected and so cannot be functionally Hausdorff.