Hyperspaces Homeomorphic to Hilbert Space

DOI10.2307/2042687zbMath0378.54004OpenAlexW4244093393MaRDI QIDQ4157659

D. W. Curtis

Publication date: 1979

Full work available at URL: https://doi.org/10.2307/2042687

Mathematics Subject Classification ID

Hyperspaces in general topology (54B20) Connected and locally connected spaces (general aspects) (54D05) Absolute neighborhood extensor, absolute extensor, absolute neighborhood retract (ANR), absolute retract spaces (general properties) (54C55) Inner product spaces and their generalizations, Hilbert spaces (46C99) Topology of infinite-dimensional manifolds (57N20)

Related Items

On a hyperspace of compact subsets which is homeomorphic to a non-separable Hilbert space, Functor \(\exp ^ c_ n\), absolute retracts and Hilbert space, Hyperspaces of finite subsets, homeomorphic to pre-Hilbert spaces, Hyperspaces of direct limits of locally compact metric spaces, Theory of retracts and infinite-dimensional manifolds, Unnamed Item, A Fake Topological Hilbert Space, On the space of Cantor subsets of \(\mathbb R^3\), On the space of \(B\)-convex compacta, On hyperspaces of max-plus and max-min convex sets, Separable complete ANR's admitting a group structure are Hilbert manifolds, Covariant functors in categories of topological spaces, Multivalued fractals, Hyperspaces of compact sets in metric linear spaces, Hyperspaces of nowhere topologically complete spaces

Cites Work

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• Characterizing Hilbert space topology
• 2^{𝑋} and 𝐶(𝑋) are homeomorphic to the Hilbert cube
• Hyperspaces of Peano continua are Hubert cubes
• Hilbert space is homeomorphic to the countable infinite product of lines
• Rétractes absolus et hyperespaces des continus