EDB — 0GW

[0GW] ¹ Let \((X, τ )\) be a topological space and let \(x_ 0 ∈ X\).

• We denote as neighbourhood of \(x_ 0\) any superset of an open set containing \(x_ 0\) .

• We call fundamental system of neighbourhoods of \(x_ 0\) a family \(\{ U_ i \} _{i∈I}\) of neighborhoods \(x_ 0\) with the property that each neighborhood of \(x_ 0\) contains at least one of the \(U_ i\) .

We will say that \(U\) is an open neighborhood of \(x_ 0\) simply to say that \(U\) is an open set that contains \(x_ 0\).