## Foundations of Point Set Theory, Volume 13, Part 1 |

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### Contents

1 | |

Consequences of Axioms 0 1 and 2 | 84 |

Consequences of Axioms 0 1 2 3 and 4 14 | 273 |

Concerning topological equivalence and the intro | 353 |

Appendix | 378 |

417 | |

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### Common terms and phrases

Amer Axioms belonging to H Cartesian plane Chapter closed and compact closed point sets closed subset collection G compact continuous curve compact continuum compact point set complementary domain connected domain connected im kleinen connected point set connected subset contains a point continuum of G countable denote the collection denote the point denote the set domain with respect elements of G endpoints exclusive closed point exists a domain exists a point exists a region exists a simple exists an arc finite set G contains G denote Hence indecomposable continuum infinite sequence intersects involves a contradiction Let K denote locally compact lying wholly mutually exclusive closed mutually exclusive continua mutually separated point nondegenerate plane point in common point of H point set obtained point sets H PROOF proper subset segment separated point sets sequence M1 set G simple closed curve simple domain subcollection subcontinuum triod upper semi-continuous collection