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A Wave Model of Metric Spaces. / Belishev, M. I.; Simonov, S. A.
в: Functional Analysis and its Applications, Том 53, № 2, 01.04.2019, стр. 79-85.Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование
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TY - JOUR
T1 - A Wave Model of Metric Spaces
AU - Belishev, M. I.
AU - Simonov, S. A.
PY - 2019/4/1
Y1 - 2019/4/1
N2 - Let Ω be a metric space. By A t we denote the metric neighborhood of radius t of a set A ⊂ Ω and by D, the lattice of open sets in Ω with partial order ⊆ and order convergence. The lattice of D-valued functions of t ∈ (0, ∞) with pointwise partial order and convergence contains the family ID = {A(·)| A(t) = A t, A ∈ D}. Let ̃Ω be the set of atoms of the order closure ID¯. We describe a class of spaces for which the set ̃Ω equipped with an appropriate metric is isometric to the original space Ω. The space ̃Ω is the key element of the construction of the wave spectrum of a lower bounded symmetric operator, which was introduced in a work of one of the authors. In that work, a program for constructing a functional model of operators of the aforementioned class was laid down. The present paper is a step in the realization of this program.
AB - Let Ω be a metric space. By A t we denote the metric neighborhood of radius t of a set A ⊂ Ω and by D, the lattice of open sets in Ω with partial order ⊆ and order convergence. The lattice of D-valued functions of t ∈ (0, ∞) with pointwise partial order and convergence contains the family ID = {A(·)| A(t) = A t, A ∈ D}. Let ̃Ω be the set of atoms of the order closure ID¯. We describe a class of spaces for which the set ̃Ω equipped with an appropriate metric is isometric to the original space Ω. The space ̃Ω is the key element of the construction of the wave spectrum of a lower bounded symmetric operator, which was introduced in a work of one of the authors. In that work, a program for constructing a functional model of operators of the aforementioned class was laid down. The present paper is a step in the realization of this program.
KW - metric space
KW - lattice of open subsets
KW - isotony
KW - lattice-valued function
KW - atom
KW - wave model
UR - http://www.scopus.com/inward/record.url?scp=85069466523&partnerID=8YFLogxK
UR - http://www.mendeley.com/research/wave-model-metric-spaces
U2 - 10.1134/S0016266319020011
DO - 10.1134/S0016266319020011
M3 - статья
VL - 53
SP - 79
EP - 85
JO - Functional Analysis and its Applications
JF - Functional Analysis and its Applications
SN - 0016-2663
IS - 2
ER -
ID: 47875495