Neighbourhood space
From HandWiki
In topology and related areas of mathematics, a neighbourhood space is a set X such that for each [math]\displaystyle{ x \in X }[/math] there is an associated neighbourhood system [math]\displaystyle{ \mathfrak{R}_x }[/math].[1]
A subset O of a neighbourhood space is called open if for every [math]\displaystyle{ x \in O }[/math] 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
References
- ↑ 1.0 1.1 Mendelson, Bert (1975). Introduction to Topology. New York: Dover. p. 77. ISBN 978-0-486-66352-4.
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