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 $X$.