## Abstract

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 ω^{μ}·m+1; it is also an image of ω^{μ}·(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 language | English |
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Pages (from-to) | 83-100 |

Number of pages | 18 |

Journal | Journal of Geometry |

Volume | 17 |

Issue number | 1 |

DOIs | |

State | Published - Dec 1981 |

## Keywords

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

## ASJC Scopus subject areas

- Geometry and Topology