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 \( {\displaystyle {\mathfrak {R}}_{x}} \) .[1]
A subset O of a neighbourhood space is called open if for every \( {\displaystyle x\in O} \) 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]
See also
neighbourhood
References
Mendelson, Bert (1975). Introduction to Topology. New York: Dover. p. 77. ISBN 978-0-486-66352-4.
Undergraduate Texts in Mathematics
Graduate Studies in Mathematics
Hellenica World - Scientific Library
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