"Continuity" properties in lattices of topological structures

  • Friedhelm Schwarz
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 871)


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.


Complete Lattice Continuous Lattice Dual Lattice Compact Element Topological Category 
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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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