1 min read

Local basis

Local basis

Local basis used for limit like this (((((((((()))))))))). A topological space can define limit if the space has countable local basis.

Definition of local basis

A collection \(\mathfrak{B}\) of Neiborhood of \(x\) such that every neiborhood of \(x\) which contains at least one element of \(\mathfrak{B}\)

Neiborhood system, Neiborhood filter (view of local basis)

Open set with neiborhood filter