Numerical meshes and covering meshes of approximate inverse systems of compacta

Abstract:

Mardešić and Rubin (1989) introduced approximate inverse systems of metric compacta by the conditions ${({\text {A}}1)^ \ast } - {({\text {A}}3)^ \ast }$. Mardešić and Watanabe (1988) introduced approximate inverse systems of topological spaces by the conditions $({\text {A}}1) - ({\text {A}}3)$. In this note we show that any approximate inverse system of metric compacta satisfies $({\text {A}}1) - ({\text {A}}3)$ if and only if it satisfies ${({\text {A}}1)^\ast } - {({\text {A}}3)^\ast }$ for some matrices (see Theorem 1).