# Hausdorff space

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## Definition

Given a Topological space [ilmath](X,\mathcal{J})[/ilmath] we say it is **Hausdorff**^{[1]} or **satisfies the Hausdorff axiom** if:

- For all [ilmath]a,b\in X[/ilmath] that are distinct there exists neighbourhoods to [ilmath]a[/ilmath] and [ilmath]b[/ilmath], [ilmath]N_a[/ilmath] and [ilmath]N_b[/ilmath] such that:
- [ilmath]N_a\cap N_b=\emptyset[/ilmath]

## References

- ↑ Introduction to topology - Mendelson - Third Edition