Embedding of the free abelian topological group A (X ⊕ X) into A (X)

Title: Embedding of the free abelian topological group A (X ⊕ X) into A (X)
Creator: Krupski, Mikolaj; Leiderman, Arkady; Morris, Sidney
Date: 2019
Type: Text; Journal article
Identifier: http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/169247
Identifier: vital:13981
Identifier: https://doi.org/10.1112/S0025579319000123
Identifier: ISBN:0025-5793
Abstract: We consider the following question: for which metrizable separable spaces X does the free abelian topological group A (X ⊕ X) isomorphically embed into A (X). While for many natural spaces X such an embedding exists, our main result shows that if X is a Cook continuum or X is a rigid Bernstein set, then A(X ⊕ X) does not embed into A(X) as a topological subgroup. The analogous statement is true for the free boolean group B (X).
Publisher: University College London
Relation: Mathematika Vol. 65, no. 3 (2019), p. 708-718
Rights: This metadata is freely available under a CCO license
Subject: 0101 Pure Mathematics; Equivalent; Spaces
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