Neighbourhood space

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In topology and related areas of mathematics, a neighbourhood space is a set X such that for each x \in X there is an associated neighbourhood system \mathfrak{R}_x.[1]

A subset O of a neighbourhood space is called open if for every x \in O 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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References[edit]

  1. ^ a b Mendelson, Bert (1975). Introduction to Topology. New York: Dover. p. 77. ISBN 978-0-486-66352-4.