Title: Theory of Compact Hausdorff Shape,
Abstract: In this paper, we aim to establish a new shape theory, compact Hausdorff
shape (CH-shape) for general Hausdorff spaces. We use the "internal" method and
direct system approach on the homotopy category of compact Hausdorff spaces.
Such a construction can preserve most good properties of H-shape given by Rubin
and Sanders. Most importantly, we can moreover develop the entire homology
theory for CH-shape, including the exactness, dual to the consequence of
Mardešić and Segal.