On some coarse shape invariants

The author and N. Uglešić have recently introduced a new classification of topological spaces, strictly coarser than the shape type classification. The corresponding coarse shape theory is founded on the coarse shape category. In this paper several topological and shape invariants are considered with respect to the coarse shape. It is shown that the coarse shape domination preserves connectedness, shape dimension, movability, n-movability and strong movability. Further, stability is a coarse shape invariant. Moreover, the coarse shape and shape coincide on the class of stable spaces.