Let Ω be a metric space. By A^t we denote the metric neighborhood of radius t of a set A ⊂ Ω and by \(\mathfrak{D}\), the lattice of open sets in Ω with partial order ⊆ and order convergence. The lattice of \(\mathfrak{D}\)-valued functions of t ∈ (0, ∞) with pointwise partial order and convergence contains the family I\(\mathfrak{D}\) = {A(·)| A(t) = A^t, A ∈ \(\mathfrak{D}\)}. Let ̃Ω be the set of atoms of the order closure \(\overline{I\mathfrak{D}}\). 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.

中文翻译：

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度量空间的波动模型

令Ω为度量空间。通过甲^吨我们表示的半径度量附近吨一组阿通过⊂Ω和\（\ mathfrak {d} \） ，的开集Ω中与偏序⊆和顺序收敛晶格。的晶格\（\ mathfrak {d} \） -valued的功能吨∈（0，∞）具有逐点偏序和收敛包含家庭我\（\ mathfrak {d} \） = {甲（·）| 甲（吨）=阿^吨，甲∈ \（\ mathfrak {d} \） }。令̃Ω为顺序闭合\（\ overline {I \ mathfrak {D}} \）的原子集。我们描述了一类空间，其中配备适当度量的集合̃Ω与原始空间Ω是等距的。空间isΩ是下界对称算子的波谱构建的关键元素，在其中一位作者的作品。在这项工作中，制定了用于构建上述类别的运营商功能模型的程序。本文是该程序实现的一步。