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Suppose the property

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

*x*} is semidecidable for each*x*So each singleton is open

Then the space is

*discrete*

Open set | = | Semidecidable property |

Closed set | = | Semidecidable complement |

Clopen set | = | Decidable property |

Continuous function | = | Computable function |

Discrete space | = | Semidecidable equality |

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