近傍系の定義

$(X, \mathcal{O}_X)$: a topological space
$x \in X$
$U \subset X$
$$ U \text{ is a neighborhood of } X \Longleftrightarrow {}^{\exists}O \in \mathcal{O} \text{, } x \in O \subset U $$ $$ \mathcal{N}_X(x) = \{ U \subset X \hspace{.20em}| \hspace{.20em} U \text{ is a neighborhood of } X \} \cdots \text{ a neighborhood system } $$