These things must be closed under arbitrary union and  nite intersection.
A suspension is de ned by the join of one of these with a pair of points. If one of these has a property named for Baire, then each of its subsets of the  rst category must have an empty interior. These things were de ned by Hausdor  using several axioms which are no longer considered necessary, such as the requirement that any two elements of these things be elements of   disjoint open sets; that is the criterion for these things to be Hausdor . These things must be closed under arbitrary union and  nite intersection. For ten points, identify these mathematical objects which de ne a collection of open sets.
A suspension is de ned by the join of one of these with a pair of points.
topologies [accept word forms, accept abstract topological spaces, prompt on spaces]