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Math and science::Topology

Neighbourhoods

Let X be a set with topology T. A neighbourhood of x is [a something that something].

This is the definition according to Munkres. Tom Leinster gives a different definition that distinguishes between a 'neighbourhood' and an 'open neighbourhood'.

Neighbourhood is the closest we get to the metric space idea of open balls around a point.

The term neighbourhood packs a noun-verb pair into a noun, which I think is part of why using it makes it easier to conceptualize compared to 'open set containing x'.