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Orderability and Suborderability Results for Totally
NonOrderability of Suborderable Spaces with Many Pseudogaps
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Amer assume base clopen closed subbase co-absolute cofinal collection collectionwise normal comments Section compact ordered space compact space contains continuous image convex set convexity components COROLLARY define definition dendron denote dense metrizable dense orderable subspace dense set disjoint Douwen elements endpoints equivalence exists finite GO-space Hahn-Mazurkiewicz theorem Hausdorff space hence hereditarily homeomorphic i e n implies intersection ISBN 90 isolated points Lemma Lindelof Lindelof space linearly ordered locally connected LOTS LUTZER MARDESIC Math metric space metrization theorem nbhd nearness space normal open set order topology ordered continuum ordered topological space ordinal p-space paracompact partial order Proc PROOF pseudogap points quasi-metric R(nX regular cardinal result scattered space sequence subcontinuum suborder suborderable space subset Suppose THEOREM topological spaces topology TREYBIG uncountable WATTEL x,y e