# regularly open

Given a topological space^{} $(X,\tau )$, a *regularly open ^{} set* is an open set $A\in \tau $ such that

$$\mathrm{int}\overline{A}=A$$ |

An example of non regularly open set on the standard topology for $\mathbb{R}$ is $A=(0,1)\cup (1,2)$ since $\mathrm{int}\overline{A}=(0,2)$.

Title | regularly open |
---|---|

Canonical name | RegularlyOpen |

Date of creation | 2013-03-22 12:19:43 |

Last modified on | 2013-03-22 12:19:43 |

Owner | drini (3) |

Last modified by | drini (3) |

Numerical id | 5 |

Author | drini (3) |

Entry type | Definition |

Classification | msc 54-00 |