ThmDex – An index of mathematical definitions, results, and conjectures.
▼ Set of symbols
▼ Alphabet
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▼ Theory
▼ Zermelo-Fraenkel set theory
▼ Set
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▼ Power set
▼ Hyperpower set sequence
▼ Hyperpower set
▼ Hypersubset
▼ Subset algebra
▼ Subset structure
▼ Topological space
Definition D93
Neighbourhood
Formulation 0
Let $T = (X, \mathcal{T})$ be a D1106: Topological space.
A D11: Set $N \subseteq X$ is a neighbourhood of $E \subseteq X$ in $T$ if and only if \begin{equation} \exists \, U \in \mathcal{T} : E \subseteq U \subseteq N \end{equation}
Children
▶ D462: Open neighbourhood