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### Contents

Elementary Set Theory I | 1 |

Ordinals and Cardinals | 29 |

Topological Spaces | 62 |

Copyright | |

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A C X A C Y a e s arbitrary Assume axiom Baire space basis bijective c-topology called cardinal cartesian product Cauchy closed map closed sets compact space completely regular completely regular space connected containing continuous map converges convex countably compact define Definition Let deformation retract denoted dense direct spectrum discrete space element equivalence relation exists extendable fiber structure filterbase finite follows given Hausdorff space homeomorphism Hurewicz fibration identity map induced injective intersection isomorphism lemma Lindelof locally compact metric space n e Z+ nbd-finite refinement nonempty nullhomotopic open covering open map open sets ordinal number paracompact path component path-connected preordered Prove real numbers regular space satisfies Section sequence simplex strong deformation retract subbasis subset subspace surjective Theorem Let topological space trivial vector space verify well-ordered