## Unified Spaces and Singular Sets for Mappings |

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### Contents

Metrizability Dimension and Characterizations | 5 |

Local Connectedness of the Unified Space | 13 |

Uni coherence of the Unified Space | 28 |

2 other sections not shown

### Common terms and phrases

11m sup boundaries of point closed and connected closed mapping closure compact boundaries compact Hausdorff space compact mapping compact open set compact set Complementation Property completes the proof conditionally compact component conditionally compact open conditionally compact region conditions of Theorem connected generalized continuum connected set connectedness continuous extension continuous map continuum lying covering dimension disjoint end let exists a conditionally exponentially representable finitely many components hence homeomorphic homeomorphio inductive dimension infinitely many compact inverses of f lcoally connected Lemma lies entirely limit point locally compact Hausdorff locally connected space locally finite covering meet infinitely metric space monotone mapping multicoherent necessary and sufficient non-compact mapping non-conditionally compact component non-empty compact components olosed one-point compactification open covering open set open subset paracompact point inverses prcof of Theorem Q containing quasi-monotone quasi-open map separable metric space singular set sufficient condition suoh Suppose that f Theorem 3.1 unicoherent weakly weakly-unicoherent Whyburn