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Characterizing non-separable sigma-locally compact infinite-dimensional manifolds and its applications

机译:不可分离的sigma-局部紧无限维流形的表征及其应用

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For an infinite cardinal τ, let ℓ_2~f(τ) be the linear span of the canonical orthonormal basis of the Hilbert space ℓ_2(τ) of weight = τ. In this paper, we give characterizations of topological manifolds modeled on ℓ_2~f(τ) and ℓ_2~f((τ) × Q, where Q = [-1, 1]~N is the Hilbert cube. We denote the full simplicial complex of cardinality = r and the hedgehog of weight = τ by Δ(τ) and J(τ) , respectively. Using our characterization of ℓ_2~f (τ) , we prove that both the metric polyhedron of Δ(τ) and the space J(τ)_f~N = {x ∈ J(τ)~N ∣ x(n) = 0 except for finitely many n ∈ N} are homeomorphic to ℓ_2~f(τ).
机译:对于无穷大的基数τ,令ℓ_2〜f(τ)是权重=τ的希尔伯特空间ℓ_2(τ)的规范正交基础的线性范围。在本文中,我们给出了以ℓ_2〜f(τ)和ℓ_2〜f((τ)×Q为模型的拓扑流形的表征,其中Q = [-1,1]〜N是希尔伯特立方体,我们表示完全单形基数= r的复合体和权重=τ的刺猬分别由Δ(τ)和J(τ)构成。利用我们对ℓ_2〜f(τ)的刻画,我们证明了Δ(τ)的度量多面体和空间J(τ)_f〜N = {x∈J(τ)〜N ∣ x(n)= 0,除了有限数量的n∈N}同胚于ℓ_2〜f(τ)。

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