- Neighbourhood space
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In topology and related areas of mathematics, a neighbourhood space is a set X such that for each
there is an associated neighbourhood system
. [1]
A subset O of a neighbourhood space is called open if for every
is a neighbourhood of x. Under this definition the open sets of a neighbourhood space give rise to a topological space. Conversely, every topological space is a neighbourhood space under the usual definition of a neighbourhood in a topological space.[1]
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