Abstract
We construct some unusual spaces by considering maximal members of suitable families of topologies. For example, we construct a countable regular crowded space no point of which is a limit point of two disjoint sets. An application to ω ∗ is that there is a separable space which is a continuous image of ω * under a ⩽ two-to-one map. We also show that for each k ϵ [2, ω), there is a k-irresolvable space.
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