Abstract:J. Keesling has shown that for connected spaces $X$ the natural inclusion $e:X\rightarrow \beta X$ of $X$ in its Stone-\v Cech compactification is a shape equivalence if and only if $X$ is pseudocompact. This paper establishes the analogous result for strong shape. Moreover, pseudocompact spaces are characterized as spaces which admit compact resolutions, which improves a result of I. Lon\v car.
Keywords: inverse system, resolution, Stone-\v Cech compactification, pseudocompact space, shape, strong shape
AMS Subject Classification: 54B35, 54C56, 54D30, 55P55