On the failure of BD-ࡃ and BD, and an application to the anti-Specker property

We give the natural topological model for \negBD-{\mathbb N}, and use it to show that the closure of spaces with the anti-Specker property under product does not imply BD-{\mathbb N}. Also, the natural topological model for \negBD is presented. Finally, for some of the realizability models known indirectly to falsify BD-\mathbb{N}, it is brought out in detail how BD-\mathbb N fails.