## A-spaces and countably bi-quotient maps |

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### Contents

Introduction | 5 |

Countably biquotient maps and their two generalizations | 9 |

Relatively pseudocompact and lightly compact subsets | 12 |

Copyright | |

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### Common terms and phrases

1-spaces accumulation point assume base of open-closed characterizations Clearly closed Bn closed map closure compact space completely regular completes the proof continuum hypothesis converges countable subsets countably bi-quotient map countably bi-sequential countably compact decreasing sequence define determined by countable Diagram 1.2 equivalent Example exists filter base first-countable space following properties follows from Theorem Frechet Hausdorff space Hence homeomorphic implies inner-closed A-space inner-closed J.-space inner-one A-space inner-one J.-space Lemma Let An\y Let Bn let us show Lindelof locally finite collection mapping properties Martin's Axiom measurable cardinality metrizable metrizable space neighborhood of xn non-measurable cardinality Nu{y open cover open subsets outer-closed outer-open A-space P-point paracompact space Pick prefixes Proposition 4.4 quotient map regular space relatively lightly compact remains true resp Section sequential sequential space single A-space single J.-space strict A-space strict J.-space super-single Suppose An\y Suppose f Theorem 6.3 topology vaguely countably bi-quotient