Imbedding One Dimensional Metric Spaces |
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Contents
Definitions and Well Known Theorems | 9 |
Constructions Analogous to the Separable Case | 13 |
Decompositions of OneDimensional Spaces | 21 |
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a,b ɛ H a₁ am+1 assumed Baire space Cantor set Cartesian product closed map collectionwise normal complete the proof Consequently contains continuous and quotient continuous quotient map defined denoted dimension less dimensional metric space dimensional space diml discrete collection discrete space Edry exists an open ɛ Bdry ɛ G finite dimensional finite open cover Hence hereditarily quotient homeomorphism implies irrational points J₂ K U F last ancestor Lemma locally finite open lord number of copies one-dimensional metric space one-to-one open collection open inverse set open set p²-inverse set perfect map points of J(t proof of Lemma Proposition 4.1 rational point remains to show separable metric space sequence of decompositions sets of form single valued space of weight subspace suffices to show tail index Theorem 1.7 topological product topological space U{Bdry unit interval University of Virginia W₁ W₂ zero-dimensional space