Characterizing non-separable sigma-locally compact infinite-dimensional manifolds and its applications
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- Koshino Katsuhisa
- Doctoral Program in Mathematics, Graduate School of Pure and Applied Sciences, University of Tsukuba
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抄録
For an infinite cardinal τ, let ℓ2f(τ) be the linear span of the canonical orthonormal basis of the Hilbert space ℓ2(τ) of weight = τ. In this paper, we give characterizations of topological manifolds modeled on ℓ2f(τ) and ℓ2f(τ) × Q, where Q = [−1,1]ℕ is the Hilbert cube. We denote the full simplicial complex of cardinality = τ and the hedgehog of weight = τ by Δ(τ) and J(τ), respectively. Using our characterization of ℓ2f(τ), we prove that both the metric polyhedron of Δ(τ) and the space<br> J(τ)ℕf = {x ∈ J(τ)ℕ | x(n) = 0 except for finitely many n ∈ ℕ}<br>are homeomorphic to ℓ2f(τ).
収録刊行物
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- Ｊｏｕｒｎａｌ ｏｆ ｔｈｅ Ｍａｔｈｅｍａｔｉｃａｌ Ｓｏｃｉｅｔｙ ｏｆ Ｊａｐａｎ
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Ｊｏｕｒｎａｌ ｏｆ ｔｈｅ Ｍａｔｈｅｍａｔｉｃａｌ Ｓｏｃｉｅｔｙ ｏｆ Ｊａｐａｎ 66 (4), 1155-1189, 2014
一般社団法人 日本数学会
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キーワード
- ℓ<sub>2</sub><sup><i>f</i></sup>(τ)-manifold
- (ℓ<sub>2</sub><sup><i>f</i></sup>(τ) × <i><b>Q</b></i>)-manifold
- (ℓ<sub>2</sub>(τ), ℓ<sub>2</sub><sup><i>f</i></sup>(τ))-manifold pair
- (ℓ<sub>2</sub>(τ) × <i><b>Q</b></i>, ℓ<sub>2</sub><sup><i>f</i></sup>(τ) × <i><b>Q</b></i>)-manifold pair
- full simplicial complex
- hedgehog
- ANR
- (strong) <i>Z</i>-set
- <i>Z</i>-embedding
- the strong universality
- the τ-discrete <i>n</i>-cells property
- the τ-discrete approximation property
詳細情報 詳細情報について
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- CRID
- 1390282680092080384
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- NII論文ID
- 130004705998
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- NII書誌ID
- AA0070177X
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- ISSN
- 18811167
- 18812333
- 00255645
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- NDL書誌ID
- 025861720
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- 本文言語コード
- en
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- データソース種別
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- JaLC
- NDL
- Crossref
- CiNii Articles
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- 抄録ライセンスフラグ
- 使用不可
