Isometric model of metric spaces

Результат исследований: Публикации в книгах, отчётах, сборниках, трудах конференцийстатья в сборнике материалов конференции

Выдержка

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.

Язык оригиналаАнглийский
Название основной публикации2018 DAYS ON DIFFRACTION (DD)
РедакторыOV Motygin, AP Kiselev, LI Goray, AY Kazakov, AS Kirpichnikova, MV Perel
ИздательIEEE Canada
Страницы274-276
Число страниц3
СостояниеОпубликовано - 2018
СобытиеInternational conference Days on Diffraction-2018 - St Petersburg, Российская Федерация
Продолжительность: 4 июн 20188 июн 2018

Конференция

КонференцияInternational conference Days on Diffraction-2018
СтранаРоссийская Федерация
ГородSt Petersburg
Период4/06/188/06/18

Цитировать

Simonov, S. (2018). Isometric model of metric spaces. В OV. Motygin, AP. Kiselev, LI. Goray, AY. Kazakov, AS. Kirpichnikova, & MV. Perel (Ред.), 2018 DAYS ON DIFFRACTION (DD) (стр. 274-276). IEEE Canada.
Simonov, Sergey. / Isometric model of metric spaces. 2018 DAYS ON DIFFRACTION (DD). редактор / OV Motygin ; AP Kiselev ; LI Goray ; AY Kazakov ; AS Kirpichnikova ; MV Perel. IEEE Canada, 2018. стр. 274-276
@inproceedings{b542c5bbb6fb4f50aebfafb63a750b0e,
title = "Isometric model of metric spaces",
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.",
author = "Sergey Simonov",
year = "2018",
language = "Английский",
pages = "274--276",
editor = "OV Motygin and AP Kiselev and LI Goray and AY Kazakov and AS Kirpichnikova and MV Perel",
booktitle = "2018 DAYS ON DIFFRACTION (DD)",
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Simonov, S 2018, Isometric model of metric spaces. в OV Motygin, AP Kiselev, LI Goray, AY Kazakov, AS Kirpichnikova & MV Perel (ред.), 2018 DAYS ON DIFFRACTION (DD). IEEE Canada, стр. 274-276, International conference Days on Diffraction-2018, St Petersburg, Российская Федерация, 4/06/18.

Isometric model of metric spaces. / Simonov, Sergey.

2018 DAYS ON DIFFRACTION (DD). ред. / OV Motygin; AP Kiselev; LI Goray; AY Kazakov; AS Kirpichnikova; MV Perel. IEEE Canada, 2018. стр. 274-276.

Результат исследований: Публикации в книгах, отчётах, сборниках, трудах конференцийстатья в сборнике материалов конференции

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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.

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Simonov S. Isometric model of metric spaces. В Motygin OV, Kiselev AP, Goray LI, Kazakov AY, Kirpichnikova AS, Perel MV, редакторы, 2018 DAYS ON DIFFRACTION (DD). IEEE Canada. 2018. стр. 274-276