Subevent of GSTT Session #7A
‟Hausdorff reflection preserves shape” by Diego Mondéjar <diego.mondejar@cunef.edu>, CUNEF Universidad
Abstract:
We study the interaction between topological reflections and shape theory. We give general conditions under which a reflection preserves shape, showing in particular that the Hausdorff reflection induces a shape equivalence. This provides a categorical interpretation of reflections as operations that do not alter the global structure of spaces at the level of shape. Applications to inverse limits of finite $T_0$ spaces are discussed, where non-Hausdorff models retain the same shape as their Hausdorff counterparts.