Topology and Order Structures, Part 1Harold R. Bennett, David John Lutzer |
Contents
LINEAR ORDERABILITY | 1 |
Orderability and Suborderability Results for Totally | 9 |
NonOrderability of Suborderable Spaces with Many Pseudogaps | 17 |
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Amer assume base clopen closed subbase co-absolute cofinal collectionwise normal comments Section compact ordered space compact space contains continuous image convex set convexity components COROLLARY countable cross-free define definition dendron denote dense orderable subspace dense set disjoint Douwen elements endpoints exists finite GO-space Hahn-Mazurkiewicz theorem Hausdorff space hence hereditarily homeomorphic i e n implies intersection ISBN 90 isolated points Lemma Lindelöf Lindelöf space linearly ordered locally connected LOTS LUTZER MARDEŠIĆ Math metric space metrization theorem nearness space neighbournet normal open set order topology ordered continuum ordered topological space ordinal p-space paracompact partial order Proc PROOF pseudogap points quasi-metrizable R(nX R₁ regular cardinal result scattered space sequence subcontinuum suborder suborderable space subset Suppose T₁ THEOREM topological spaces topology TREYBIG U₁ uncountable w₁ WATTEL x,y e α α α