A topological space \(X\) is said to be path connected if for two give points \(p,q\in X\) there is continuous function \(f\colon [0,1]\to X\) with \(f(0)=p\) and \(f(1)=q\). The function \(f\) is usually called path.
Example
A topological space \(X\) is said to be path connected if for two give points \(p,q\in X\) there is continuous function \(f\colon [0,1]\to X\) with \(f(0)=p\) and \(f(1)=q\). The function \(f\) is usually called path.