more intuitive is that in terms of [[Neighbourhood (mathematics) and so this is given first.

Definition via neighbourhoods

This axiomatization is due to Felix Hausdorff.Let be a (possibly empty) set. The elements of are usually called points, though they can be any mathematical object. Let be a function assigning to each (point) in a non-empty collection of subsets of The elements of will be called neighbourhoods of with respect

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