## Metrizability in generalized ordered spaces |

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### Contents

INTRODUCTION | |

LOTSs AND GOSPACES 8 | ii |

METRIZABILITY IN GOspaces | 47 |

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a-discrete family a-r-discrete a<u a Baire space choose x e Clearly closed subset cofinal coinitial compact Consequently consisting of convex constitutes a a-discrete continuous mapping convex open neighbourhood convex sets convex subset convexity-component under f COROLLARY countable chain condition countable local base denote dense subset exists a convex finite following properties Furthermore GO-space GO-topology Hence hereditarily Lindelof homeomorphic integer isolated points left endpoint left neighbour lemma Let f lexicographic product lexicographically ordered product limit ordinal Lindelof space linearly ordered set LOTS's Lutzer metric space Moreover mutually disjoint non-isolated open cover open intervals open sets open subsets order-topology ordinal number paracompact space perfectly normal point p e possesses neighbourpoints PROOF pseudo-gap relatively discrete subset right endpoint right neighbour Sorgenfrey-line subspace suppose THEOREM topological space uncountable