Lines, trees, and branch spaces

Harold Bennett, David Lutzer, Mary Ellen Rudin

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

In this paper we examine the interactions between the topology of certain linearly ordered topological spaces (LOTS) and the properties of trees in whose branch spaces they embed. As one example of the interaction between ordered spaces and trees, we characterize hereditary ultraparacompactness in a LOTS (or GO-space) X in terms of the possibility of embedding the space X in the branch space of a certain kind of tree.

Original languageEnglish
Pages (from-to)367-384
Number of pages18
JournalOrder
Volume19
Issue number4
DOIs
StatePublished - 2002

Keywords

  • Branch space
  • GO-space
  • Generalized ordered space
  • LOTS
  • Linearly ordered topological space
  • Souslin space
  • Tree
  • Ultraparacompact

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