Definition 3.3.1 (Neighbourhood).label Let $(X,\Tc)$ be a topological space and $A\suf X$. A neighborhood of $A$ is a set $V\in\cali{P}(X)$ such that there exists $U\in\Tc$ satisfying $A\suf U\suf V\suf X$.

Denote by $\cali{N}_{X,\Tc}(A)=\cali{N}_{X}(A)=\cali{N}(A)$ the collection of all Neighbourhoods of $A$, and $\cali{N}^{o}(A)$ the collection of open neighborhoods of $A$.

If $A=\curl{x}$ for some $x\in X$ then the above definition applies to $x$ directly.