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Applications of maximal topologies. (English) Zbl 0845.54028
Summary: Some unusual spaces are constructed by considering maximal members of suitable families of topologies. For example, there is constructed a countable regular crowded space no point of which is a limit point of two disjoint sets. An application to \(\omega^*\) is that there is a separable space which is a continuous image of \(\omega^*\) under a \(\leq\)two-to-one map. It is also shown that for each \(k\in [2,\omega)\), there is a \(k\)-irresolvable space.

MSC:
54G15 Pathological topological spaces
54C05 Continuous maps
54A10 Several topologies on one set (change of topology, comparison of topologies, lattices of topologies)
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