Abstract
In this paper, we extend the concepts of movability, strong movability, AWR and AWNR for arbitrary metrizable spaces and we show that MAR and AWR are the same concept and that MANR, strong movability and movable AWNR are the same concept. And we prove that the projection of the product X × Y of a locally compact metric space X and an MAR Y onto X induces the shape equivalence and that the inclusion of a metric space X into a union X \cup Y of X and an MAR Y induces a shape equivalence if X and Y are closed in X \cup Y and if X \cap Y is an MAR.
