Abstract
Consider the C-fibre of an infinite set X (i.e. the set of all C-structures on X) for some bireflective or bicoreflective subcategory C of the topological spaces. If we define the order by the continuity of the identity map, then only the A-topologies and the partition topologies yield continuous lattices. None of the dual lattices is continuous. In particular, with respect to neither order, the topologies on X form a continuous lattice. The limitierungen on X form a continuous lattice with respect to the order defined above, but not with respect to the dual one.
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© 1981 Springer-Verlag
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Schwarz, F. (1981). "Continuity" properties in lattices of topological structures. In: Banaschewski, B., Hoffmann, RE. (eds) Continuous Lattices. Lecture Notes in Mathematics, vol 871. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0089916
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DOI: https://doi.org/10.1007/BFb0089916
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