Isometric model of metric spaces

Research outputpeer-review

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 languageEnglish
Title of host publication2018 DAYS ON DIFFRACTION (DD)
EditorsOV Motygin, AP Kiselev, LI Goray, AY Kazakov, AS Kirpichnikova, MV Perel
PublisherIEEE Canada
Pages274-276
Number of pages3
Publication statusPublished - 2018
EventInternational conference Days on Diffraction-2018 - St Petersburg
Duration: 4 Jun 20188 Jun 2018

Conference

ConferenceInternational Conference on Days on Diffraction (DD)
CountryRussian Federation
CitySt Petersburg
Period4/06/188/06/18

Cite this

Simonov, S. (2018). Isometric model of metric spaces. In OV. Motygin, AP. Kiselev, LI. Goray, AY. Kazakov, AS. Kirpichnikova, & MV. Perel (Eds.), 2018 DAYS ON DIFFRACTION (DD) (pp. 274-276). IEEE Canada.
Simonov, Sergey. / Isometric model of metric spaces. 2018 DAYS ON DIFFRACTION (DD). editor / OV Motygin ; AP Kiselev ; LI Goray ; AY Kazakov ; AS Kirpichnikova ; MV Perel. IEEE Canada, 2018. pp. 274-276
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author = "Sergey Simonov",
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editor = "OV Motygin and AP Kiselev and LI Goray and AY Kazakov and AS Kirpichnikova and MV Perel",
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Simonov, S 2018, Isometric model of metric spaces. in OV Motygin, AP Kiselev, LI Goray, AY Kazakov, AS Kirpichnikova & MV Perel (eds), 2018 DAYS ON DIFFRACTION (DD). IEEE Canada, pp. 274-276, St Petersburg, 4/06/18.

Isometric model of metric spaces. / Simonov, Sergey.

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

Research outputpeer-review

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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. In Motygin OV, Kiselev AP, Goray LI, Kazakov AY, Kirpichnikova AS, Perel MV, editors, 2018 DAYS ON DIFFRACTION (DD). IEEE Canada. 2018. p. 274-276