On \({\mathbb{R}}^{\infty}\)-manifolds and \(Q^{\infty}\)-manifolds

DOI10.1016/0166-8641(84)90032-4zbMath0568.57014OpenAlexW2056778790MaRDI QIDQ1060469

Katsuro Sakai

Publication date: 1984

Published in: Topology and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0166-8641(84)90032-4

zbMATH Keywords

near homeomorphismopen embedding\({\mathbb{R}}^{\infty }\)-manifold\(Q^{\infty }\)-manifoldcountable direct limits of compact metric spacesfine homotopy equivalenceZ-set in the Hilbert cube

Mathematics Subject Classification ID

Embeddings and immersions in topological manifolds (57N35) Spectra in general topology (54B35) Absolute neighborhood extensor, absolute extensor, absolute neighborhood retract (ANR), absolute retract spaces (general properties) (54C55) Topology of infinite-dimensional manifolds (57N20) Homotopy and topological questions for infinite-dimensional manifolds (58B05)

Related Items (14)

Combinatorial infinite-dimensional manifolds and \({\mathbb{R}}^{\infty}\)- manifolds ⋮ Simplicial complexes triangulating infinite-dimensional manifolds ⋮ Hyperspaces of direct limits of locally compact metric spaces ⋮ Detecting topological groups which are (locally) homeomorphic to LF-spaces ⋮ Topology of manifolds modeled on countable direct limits of Menger compacta ⋮ Describing topology on the set of persistence diagrams ⋮ Infinite-dimensional hyperspaces of convex bodies of constant width ⋮ Parametric results for certain infinite-dimensional manifolds ⋮ A topological characterization of \(LF\)-spaces ⋮ All Autohomeomorphisms of Connected Menger Manifolds are Stable ⋮ Unnamed Item ⋮ Infinite-dimensional manifolds related to C-spaces ⋮ A \(Q^ \infty\)-manifold topology of the space of Lipschitz maps ⋮ On topological spaces and topological groups with certain local countable networks

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Examples of cell-like decompositions of the infinite-dimensional manifolds sigma and Sigma
• An \(\alpha\)-approximation theorem for \(R^{\infty}\)-manifolds
• On the topology of direct limits of ANR's
• An alpha-approximation theorem for \(Q^\infty\)-manifolds
• Manifolds modelled on the direct limit of lines
• On Infinite Deficiency in R ∞ -Manifolds
• Characterizing the Topology of Infinite-Dimensional σ-Compact Manifolds
• An Unknotting Theorem in Q ∞ -Manifolds
• Manifolds Modelled on R ∞ or Bounded Weak- ∗ Topologies
• A Factorization of the Direct Limit of Hilbert Cubes
• Stability, open embeddings, and classification of bounded weak-∗ manifolds
• Open Subsets of R ∞ are Stable
• On CE-images of the Hubert cube and characterization of Q-manifolds
• Contracting Spaces of Maps on the Countable Direct Limit of a Space
• Topological classification of infinite dimensional manifolds by homotopy type
• A simplicial complex whose product with any ANR is a simplicial complex
• Local properties of topological spaces

This page was built for publication: On \({\mathbb{R}}^{\infty}\)-manifolds and \(Q^{\infty}\)-manifolds