The Bow - Tie Space
March 30, 2023 • Explore
The Bow-Tie Topological Space: An Example of a Non-Hausdorff Space
In topology, there are many interesting examples of spaces that behave in unexpected ways. One such example is the bow-tie topological space, which is a non-Hausdorff space that has two disjoint closed sets whose closures intersect. In this note we outline the construction and basic properties.
Construction
Take two copies of the real line R and R' and identify 0 ∈ R with 0' ∈ R'. Endow the quotient with the topology generated by open intervals away from the origins and sets that include the identified points with the natural pieces from each copy. See the original write-up for details.
Source markdown: original upload.