### Abstract

Let Omega be a metric space and D be the lattice of its open sets with the partial order subset of, equipped with the order topology. For a set A subset of Omega, let A(t) denote its metric t-neighborhood. In the lattice of D-valued functions on (0, + infinity), consider the family ID = {A (.) vertical bar A(t) = A(t), A is an element of D}. Let (Omega) over tilde be the set of atoms of its closure, (ID) over bar, in the topology of pointwise convergence. Under certain conditions one can define a metric on (Omega) over tilde. We describe a class of metric spaces Omega such that (Omega) over tilde is isometric to Omega.

Original language | English |
---|---|

Title of host publication | 2018 DAYS ON DIFFRACTION (DD) |

Editors | OV Motygin, AP Kiselev, LI Goray, AY Kazakov, AS Kirpichnikova, MV Perel |

Publisher | IEEE Canada |

Pages | 274-276 |

Number of pages | 3 |

Publication status | Published - 2018 |

Event | International conference Days on Diffraction-2018 - St Petersburg Duration: 4 Jun 2018 → 8 Jun 2018 |

### Conference

Conference | International Conference on Days on Diffraction (DD) |
---|---|

Country | Russian Federation |

City | St Petersburg |

Period | 4/06/18 → 8/06/18 |

### Cite this

*2018 DAYS ON DIFFRACTION (DD)*(pp. 274-276). IEEE Canada.

}

*2018 DAYS ON DIFFRACTION (DD).*IEEE Canada, pp. 274-276, St Petersburg, 4/06/18.

**Isometric model of metric spaces.** / Simonov, Sergey.

Research output › › peer-review

TY - GEN

T1 - Isometric model of metric spaces

AU - Simonov, Sergey

PY - 2018

Y1 - 2018

N2 - Let Omega be a metric space and D be the lattice of its open sets with the partial order subset of, equipped with the order topology. For a set A subset of Omega, let A(t) denote its metric t-neighborhood. In the lattice of D-valued functions on (0, + infinity), consider the family ID = {A (.) vertical bar A(t) = A(t), A is an element of D}. Let (Omega) over tilde be the set of atoms of its closure, (ID) over bar, in the topology of pointwise convergence. Under certain conditions one can define a metric on (Omega) over tilde. We describe a class of metric spaces Omega such that (Omega) over tilde is isometric to Omega.

AB - Let Omega be a metric space and D be the lattice of its open sets with the partial order subset of, equipped with the order topology. For a set A subset of Omega, let A(t) denote its metric t-neighborhood. In the lattice of D-valued functions on (0, + infinity), consider the family ID = {A (.) vertical bar A(t) = A(t), A is an element of D}. Let (Omega) over tilde be the set of atoms of its closure, (ID) over bar, in the topology of pointwise convergence. Under certain conditions one can define a metric on (Omega) over tilde. We describe a class of metric spaces Omega such that (Omega) over tilde is isometric to Omega.

M3 - статья в сборнике материалов конференции

SP - 274

EP - 276

BT - 2018 DAYS ON DIFFRACTION (DD)

A2 - Motygin, OV

A2 - Kiselev, AP

A2 - Goray, LI

A2 - Kazakov, AY

A2 - Kirpichnikova, AS

A2 - Perel, MV

PB - IEEE Canada

ER -