# sequentially continuous

Let $X,Y$ be topological spaces^{}. Then a $f:X\to Y$ is said to be *sequentially continuous* if for every convergent sequence ${x}_{n}\to x$ in $X$, $f({x}_{n})\to f(x)$ in $Y$.

Every continuous function^{} is sequentially continuous, however the converse^{} is true only in first-countable spaces (for example in metric spaces).

Title | sequentially continuous |
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Canonical name | SequentiallyContinuous |

Date of creation | 2013-03-22 16:31:17 |

Last modified on | 2013-03-22 16:31:17 |

Owner | ehremo (15714) |

Last modified by | ehremo (15714) |

Numerical id | 6 |

Author | ehremo (15714) |

Entry type | Definition |

Classification | msc 54C05 |