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"Continuity" properties in lattices of topological structures

  • Friedhelm Schwarz
Conference paper
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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Copyright information

© Springer-Verlag 1981

Authors and Affiliations

  • Friedhelm Schwarz
    • 1
  1. 1.Institut für MathematikUniversität HannoverHannover 1Federal Republic of Germany

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