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"Continuity" properties in lattices of topological structures

Part of the Lecture Notes in Mathematics book series (LNM,volume 871)

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.

Keywords

  • Complete Lattice
  • Continuous Lattice
  • Dual Lattice
  • Compact Element
  • Topological Category

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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  • Print ISBN: 978-3-540-10848-1

  • Online ISBN: 978-3-540-38755-8

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