Selected Ordered Space Problems
نویسندگان
چکیده
A generalized ordered space (a GO-space) is a triple (X, τ,<) where (X,<) is a linearly ordered set and τ is a Hausdorff topology on X that has a base of order-convex sets. If τ is the usual open interval topology of the order <, then we say that (X, τ,<) is a linearly ordered topological space (LOTS). Besides the usual real line, probably the most familiar examples of GO-spaces are the Sorgenfrey line, the Michael line, the Alexandroff double arrow, and various spaces of ordinal numbers. In this paper, we collect together some of our favorite open problems in the theory of ordered spaces. For many of the questions, space limitations restricted us to giving only definitions and references for the question. For more detail, see [5]. Notably absent from our list are problems about orderability, about products of special ordered spaces, about continuous selections of various kinds, and about Cp-theory, and for that we apologize. Throughout the paper, we reserve the symbols R,P, and Q for the usual sets of real, irrational, and rational numbers respectively.
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