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Suppose the property

*N*_{x}(*y*) = (*x*≠*y*) is semidecidable for each*x*Then the set {

*x*} is closed for each*x*Then the space is Hausdorff

Open set | = | Semidecidable property |

Closed set | = | Semidecidable complement |

Clopen set | = | Decidable property |

Continuous function | = | Computable function |

Discrete space | = | Semidecidable equality |

Hausdorff space | = | Semidecidable inequality |

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