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
