ALEXANDROFF SPACES VIA SIMPLICIAL COMPLEXES
We prove that an Alexandroff space is homotopy equivalent to its shadow space. Previously, simplicial complexes and beat points have been studied on finite spaces. We extend these studies to the infinite case. Along the way, we develop the concepts of beat points and minimal spaces by introducing concepts of super beats and super minimal spaces. We give conditions on a flag simplicial complex to be an ordered simplicial complex.
Alexandroff topological space, UB space, poset, beat point, homotopy type.