# proximity continuous

Let $(P,\delta )$ and $(Q,\u03f5)$ be proximity spaces.

A function $f:P\to Q$ is said to be *proximity continuous* if for any subsets $A,B\subseteq P$, $A\mathit{\delta}B$ implies that $f(A)\mathit{\u03f5}f(B)$.

Title | proximity continuous |
---|---|

Canonical name | ProximityContinuous |

Date of creation | 2013-03-22 16:56:12 |

Last modified on | 2013-03-22 16:56:12 |

Owner | porton (9363) |

Last modified by | porton (9363) |

Numerical id | 12 |

Author | porton (9363) |

Entry type | Definition |

Classification | msc 54C08 |

Classification | msc 54C05 |

Classification | msc 54E17 |

Classification | msc 54E05 |

Synonym | near-continuousness |

Defines |
$\delta $-continuous^{} |