A Fake Topological Hilbert Space

DOI10.2307/1998961zbMath0508.54013OpenAlexW4235657944MaRDI QIDQ4746462

Jan van Mill, D. W. Curtis, R. D. Anderson

Publication date: 1982

Full work available at URL: https://doi.org/10.2307/1998961

zbMATH Keywords

Hilbert cubenegligibilitycountable dense homogeneitydiscrete approximation propertystrong local homogeneitynonhomeomorphy to the Hilbert space l2topologically complete separable metric absolute retract

Mathematics Subject Classification ID

Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with semidefinite inner product) (46C05) Topological characterizations of particular spaces (54F65) Counterexamples in general topology (54G20) Absolute neighborhood extensor, absolute extensor, absolute neighborhood retract (ANR), absolute retract spaces (general properties) (54C55) Topology of infinite-dimensional manifolds (57N20)

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Stability of a fake topological Hilbert space ⋮ Fake Boundary Sets in the Hilbert Cube ⋮ Analytic groups and pushing small sets apart ⋮ Open problems on countable dense homogeneity ⋮ Group action and shift-compactness ⋮ Representing countable groups by homeomorphism groups in Hilbert space ⋮ A Rigid Space Whose Square is the Hilbert Space ⋮ Strong Local Homogeneity Does not Imply Countable Dense Homogeneity ⋮ General Position Properties Satisfied by Finite Products of Dendrites ⋮ The topology of ultrafilters as subspaces of \(2^{\omega }\) ⋮ Dense Embeddings of Sigma-Compact, Nowhere Locally Compact Metric Spaces ⋮ Countable dense homogeneity and the Baire property ⋮ Normal systems over ANR's, rigid embeddings and nonseparable absorbing sets ⋮ Hyperspaces of separable Banach spaces with the Wijsman topology ⋮ Another Counterexample in ANR Theory ⋮ Dense embeddings of nowhere locally compact separable metric spaces ⋮ Characterization of Hilbert space manifolds revisited ⋮ Topology of actions and homogeneous spaces ⋮ Boundary sets in the Hilbert cube ⋮ Convex Hilbert cubes in superextensions

Cites Work

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