Lines, Trees, and Branch Spaces

: 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. Key words and phrases: linearly ordered topological space, LOTS, generalized ordered space, GO-space, tree, branch space, ultraparacompact, Souslin space. MR numbers: Primary = 54F05; Secondary = 54D20, 06A05, 05C05

• Type: Journal
• Year: 2002
• Where: ORDER
• Authors: Harold Bennett, David Lutzer, Mary Ellen Rudin
• Keywords: Linearly Ordered, ORDER 2002, Space, Topological Space