A countable dense homogeneous space with a dense rigid open subspace
We show that there is a Polish space which is countable dense homogeneous but contains a dense open rigid connected subset. This answers several questions of Fitzpatrick and Zhou.
We show that there is a Polish space which is countable dense homogeneous but contains a dense open rigid connected subset. This answers several questions of Fitzpatrick and Zhou.
An approach to construction of topological invariants of the Reshetikhin-Turaev-Witten type of 3- and 4-dimensional manifolds in the framework of SU(2) Chern-Simons gauge theory and its hidden (quantum) gauge symmetry is presented.
We prove that a space M with Disjoint Disk Property is a Q-manifold if and only if M × X is a Q-manifold for some C-space X. This implies that the product M × I² of a space M with the disk is a Q-manifold if and only if M × X is a Q-manifold for some C-space X. The proof of these theorems exploits the homological characterization of Q-manifolds due to Daverman and Walsh, combined with the existence of G-stable points in C-spaces. To establish the existence of such points we prove (and afterward...