# ladder connected

Definition
Suppose $X$ is a topological space^{}. Then
$X$ is called ladder connected provided that any
open cover $\mathcal{U}$ of $X$ has the following property:
If $p,q\in X$, then there exists a finite number of
open sets ${U}_{1},\mathrm{\dots},{U}_{N}$ from $\mathcal{U}$ such that
$p\in {U}_{1}$, ${U}_{1}\cap {U}_{2}\ne \mathrm{\varnothing}$, $\mathrm{\dots}$ , ${U}_{N-1}\cap {U}_{N}\ne \mathrm{\varnothing}$,
and $q\in {U}_{N}$.

Title | ladder connected |
---|---|

Canonical name | LadderConnected |

Date of creation | 2013-03-22 14:00:29 |

Last modified on | 2013-03-22 14:00:29 |

Owner | mathcam (2727) |

Last modified by | mathcam (2727) |

Numerical id | 6 |

Author | mathcam (2727) |

Entry type | Definition |

Classification | msc 54-00 |

Related topic | CharacterizationOfConnectedCompactMetricSpaces |