locally path-connected space
A topological space is called locally path-connected if it has a basis of path-connected neighbourhoods. In other words, if for every point and neighbourhood , there exists a path-connected neighbourhood that contains .
A locally path-connected space is connected if and only if it is path-connected. In any case, the connected components of a locally path-connected space are the same as its path-connected components.
The condition is a necessary assumption in the
in the form of the condition for
Revised on January 24, 2017 08:36:39
by Urs Schreiber