Axiom:Neighborhood Space Axioms

Axioms
A neighborhood space is a set $S$ such that, for each $x \in S$, there exists a set of subsets $\mathcal N_x$ of $S$ satisfying the following conditions:

These stipulations are called the neighborhood space Axioms.

Each element of $\mathcal N_x$ is called a neighborhood of $x$.

Also see

 * Basic Properties of Neighborhood in Topological Space