Thick Spanier groups and the first shape group

Abstract

We develop a new route through which to explore $\ker \Psi_{X}$, the kernel of the $\pi_{1}$-shape group homomorphism determined by a general space $X$, and establish, for each locally path connected, paracompact Hausdorff space $% X$, $\ker\Psi_{X}$ is precisely the Spanier group of $X$.