Let \(X\) be a topological space and \(p\in X\). We call a sequence \((U_i)\) of neighbourhoods of \(p\) nested neighbourhood basis if \(U_{i+1}\subseteq U_i\) for each \(i\), and every neighbourhood of \(p\) contains \(U_i\) for some \(i\).
Remark
- Every nested neighbourhood basis is a countable neighbourhood basis .