An Infinite-Dimensional Pre-Hilbert Space not Homeomorphic to its own Square

DOI10.2307/2044492zbMath0528.54032OpenAlexW4256734676MaRDI QIDQ3308682

Roman Pol

Publication date: 1984

Full work available at URL: https://doi.org/10.2307/2044492

zbMATH Keywords

Baire category theoremanalytic setEffros Borel structureBernstein-like direct sum decompositionsinfinite-dimensional separable complete linear metric spacelinearly independent Cantor sets

Mathematics Subject Classification ID

Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with semidefinite inner product) (46C05) Dimension theory in general topology (54F45) Spectra in general topology (54B35) Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets) (54H05)

Related Items (7)

Linear Spaces, Absolute Retracts, and the Compact Extension Property ⋮ Compactness is not preserved by the t-equivalence relation ⋮ Spaces of continuous functions on ordinals and ultrafilters ⋮ Final compactness is not preserved under products of spaces of the form \(C_ p(X)\) ⋮ Algebraic objects generated by topological structure ⋮ Domain Invariance in Infinite-Dimensional Linear Spaces ⋮ A countable dense homogeneous topological vector space is a Baire space

Cites Work

• Almost every function is independent
• Applications of the Baire-category method to the problem of independent sets
• Independent sets in topological algebras
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