Linear Maps do not Preserve Countable-Dimensionality

DOI10.2307/2045541zbMath0585.46018OpenAlexW4247214786MaRDI QIDQ3711020

Jerzy Mogilski, Mladen Bestvina

Publication date: 1985

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2307/2045541

zbMATH Keywords

Hamel basisembeddings onto linearly independent setslinear maps do not preserve countable-dimensionality

Mathematics Subject Classification ID

Homotopy equivalences in algebraic topology (55P10) Sequence spaces (including Köthe sequence spaces) (46A45) Classical Banach spaces in the general theory (46B25) Linear operators on special spaces (weighted shifts, operators on sequence spaces, etc.) (47B37) Dimension theory in general topology (54F45) Embedding (54C25)

Related Items (5)

Universal map of \(\sigma\) onto \(\Sigma\) and absorbing sets in the classes of absolute Borelian and projective finite-dimensional spaces ⋮ Universal finite-to-one map and universal countable dimensional spaces ⋮ Applying Coordinate Products to the Topological Identification of Normed Spaces ⋮ Function spaces homeomorphic to the countable product of \(\ell ^ f_ 2\) ⋮ Constructing space-filling curves of compact connected manifolds

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