# Simply connected topological space

Not to be confused with: a contractible topological space

## Definition

Let [ilmath](X,\mathcal{ J })[/ilmath] be a topological space, we say [ilmath]X[/ilmath] is simply connected if[1]:

## Notes

1. Notice we do not specify the basepoint of the fundamental group here, that is we write [ilmath]\pi_1(X)[/ilmath] not [ilmath]\pi_1(X,x_0)[/ilmath] for some [ilmath]x_0\in X[/ilmath], that is because for a path-connected topological space all the fundamental groups are isomorphic