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  5. 2026

General and Set-Theoretic Topology

Icon: calendar GSTT Session Talk #7A.2 | 2026 Jul 15 from 11:00AM to 11:25AM (Zagreb) | B3-16

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.