Ordinals and scattered compact ordered spaces

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Scattered Compact Ordered Spaces (SCOS) are studied with respect to their well ordered images and preimages. Typical results: (i) A SCOS is homeomorphic to an ordinal iff it has no pit point (a pit in an ordered space is one with infinite left and right cofinalities, one of which is uncountable). (ii) A SCOS of characteristic <μ,m> is mappable onto and includes ωμ·m+1; it is also an image of ωμ·(2m)+1. The SCOSs are characterized by: Theorem 5: Let K be a Hausdorff space. The following conditions are equivalent: (a) K is homeomorphic to a compact scattered ordered space. (b) K is an order-two image of a compact ordinal. A.M.S. (MOS) Subject Classification: Primary: 54F05, 54F65, 06A45 Secondary: 54D30.

Original languageEnglish
Pages (from-to)83-100
Number of pages18
JournalJournal of Geometry
Issue number1
StatePublished - Dec 1981


  • Compact well-ordered space
  • Order-two image
  • Order-two mapping
  • Scattered compact ordered space

ASJC Scopus subject areas

  • Geometry and Topology


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