Some Examples in Shape Theory Using the Theory of Compact Connected Abelian Topological Groups

Abstract

In previous papers the author has studied the shape of compact connected abelian topological groups. This study has led to a number of theorems and examples in shape theory. In this paper a theorem is proved concerning the Čech homology of compact connected abelian topological groups. This theorem together with the author’s previous results are then used to study the movability of general compact Hausdorff spaces. In the theory of shape for compact metric spaces, a number of significant theorems have been proved for movable compact metric spaces. Among these are a theorem of Hurewicz type due to K. Kuperberg, a Whitehead type theorem due to Moszyńska, and a theorem concerning the exactness of the Čech homology sequence for movable compact metric pairs due to Overton. In this paper examples are constructed which show that these theorems do not generalize to arbitrary movable compact Hausdorff spaces without additional assumptions.