## 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 |

1 other sections not shown

### Common terms and phrases

a p inverse set ancestor assumed Bdry Cantor set Cartesian product space Classical Imbedding Theorem closed map closed sets commutative diagram complete the proof continuous and quotient continuous quotient map defined denoted diagram dimension less dimensional metric space dimensional space diml discrete collection discrete space Edry equivalence class exists an open exists k(m f-inverse finite dimensional finite number finite open cover follows from statement Hence hereditarily quotient homeomorphism inclusion irrational points K U F ker(p locally finite open lord lst-ancestor number of copies one-dimensional metric space one-to-one open collection open inverse set open set open subset perfect map points of J(t proof of Lemma Proposition 4.1 rational points separable metric space sets of form single valued space J(t space of weight suffices to show tail index Theorem 1.7 tion topological product topological space transfinite construction two-to-one U{Bdry unit interval universal zero-dimensional University of Virginia Wf(a zero-dimensional space