Smallest weakly contractible non-contractible topological spaces
Nicolás Cianci, Miguel Ottina · Proceedings of the Edinburgh Mathematical Society · 2019
Abstract We characterize the topological spaces of minimum cardinality which are weakly contractible but not contractible. This is equivalent to finding the non-dismantlable posets of minimum cardinality such that the geometric realization of their order complexes are contractible. Specifically, we prove that all weakly contractible topological spaces with fewer than nine points are contractible. We also prove that there exist (up to homeomorphism) exactly two topological spaces of nine points which are weakly contractible but not contractible.