A question about the topological sphere theorem

Question

I have referred Wikipedia on the topological sphere theorem:If $M$ is a complete, simply-connected, $n$-dimensional Riemannian manifold with sectional curvature taking values in the interval $(1,4]$ then $M$ is homeomorphic to the $n$-sphere. Actually, it's true for all sectional curvatures in the interval $(1/4c,c]$,where $c$ is any positive constant. So why Wikipedia gives so special situation? Thanks in advance!