Lines,Trees, and Branch Spaces |
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| Authors: | Bennett Harold Lutzer David Rudin Mary Ellen |
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| Affiliation: | (1) Texas Tech University, Lubbock, TX, 79409, U.S.A;(2) College of William and Mary, Williamsburg, VA, 23187-8795, U.S.A;(3) University of Wisconsin, Madison, WI, 53706-1388, U.S.A |
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| 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. |
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| Keywords: | linearly ordered topological space LOTS generalized ordered space GO-space tree branch space ultraparacompact Souslin space |
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