On the Failure of BD-N and BD, and an Application to the Anti-Specker Property

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