# 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