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3-manifold 3-space 3-sphere Amer aposyndetic approximation theorem Arens Banach algebra boundary bounded characterization closed subset compact Hausdorff space compact space complementary domain connected sets contains continuous collection continuous curve continuous functions countable decomposition space defined denote differentiable dimension dimensional disk Eldon Dyer elements of G equivalent Euclidean example exists extension fiber finite number fixed point property Hausdorff space homeomorphism homogeneous homology imbedded indecomposable integer intersect isomorphic locally compact locally connected M. L. Curtis manifold mapping f Mathematics maximal ideal metric space Moise monotone neighborhood non-degenerate omorphism open covering open mapping open set orbit paracompact spaces plane continuum point set positive number problem Proc proof proved pseudo-arc quasi-complexes question R. D. Anderson R. H. Bing real-valued ring semi-metric space Seminar separate the plane sequence shown simple closed curve sphere structure subcontinuum Suppose topological space triangulated universal curve upper semi-continuous Whyburn