EMBEDDING OF THE FREE ABELIAN TOPOLOGICAL GROUP A(X⊕X) INTO A(X)

Mikołaj Krupski; Arkady Leiderman; Sidney Morris

doi:10.1112/S0025579319000123

EMBEDDING OF THE FREE ABELIAN TOPOLOGICAL GROUP A(X⊕X) INTO A(X)

Mikołaj Krupski, Arkady Leiderman, Sidney Morris

Department of Mathematics

Ben-Gurion University of the Negev

Research output: Contribution to journal › Article › peer-review

Abstract

We consider the following question: for which metrizable separable spaces (Formula presented.) does the free abelian topological group (Formula presented.) isomorphically embed into (Formula presented.). While for many natural spaces (Formula presented.) such an embedding exists, our main result shows that if (Formula presented.) is a Cook continuum or (Formula presented.) is a rigid Bernstein set, then (Formula presented.) does not embed into (Formula presented.) as a topological subgroup. The analogous statement is true for the free boolean group (Formula presented.).

Original language	American English
Pages (from-to)	708-718
Number of pages	11
Journal	Mathematika
Volume	65
Issue number	3
DOIs	https://doi.org/10.1112/S0025579319000123
State	Published - 1 Jan 2019

Keywords

22A05
54F15 (primary)

All Science Journal Classification (ASJC) codes

General Mathematics

Access to Document

10.1112/S0025579319000123

Cite this

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title = "EMBEDDING OF THE FREE ABELIAN TOPOLOGICAL GROUP A(X⊕X) INTO A(X)",

abstract = "We consider the following question: for which metrizable separable spaces (Formula presented.) does the free abelian topological group (Formula presented.) isomorphically embed into (Formula presented.). While for many natural spaces (Formula presented.) such an embedding exists, our main result shows that if (Formula presented.) is a Cook continuum or (Formula presented.) is a rigid Bernstein set, then (Formula presented.) does not embed into (Formula presented.) as a topological subgroup. The analogous statement is true for the free boolean group (Formula presented.).",

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author = "Miko{\l}aj Krupski and Arkady Leiderman and Sidney Morris",

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year = "2019",

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AU - Morris, Sidney

PY - 2019/1/1

Y1 - 2019/1/1

N2 - We consider the following question: for which metrizable separable spaces (Formula presented.) does the free abelian topological group (Formula presented.) isomorphically embed into (Formula presented.). While for many natural spaces (Formula presented.) such an embedding exists, our main result shows that if (Formula presented.) is a Cook continuum or (Formula presented.) is a rigid Bernstein set, then (Formula presented.) does not embed into (Formula presented.) as a topological subgroup. The analogous statement is true for the free boolean group (Formula presented.).

AB - We consider the following question: for which metrizable separable spaces (Formula presented.) does the free abelian topological group (Formula presented.) isomorphically embed into (Formula presented.). While for many natural spaces (Formula presented.) such an embedding exists, our main result shows that if (Formula presented.) is a Cook continuum or (Formula presented.) is a rigid Bernstein set, then (Formula presented.) does not embed into (Formula presented.) as a topological subgroup. The analogous statement is true for the free boolean group (Formula presented.).

KW - 22A05

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DO - 10.1112/S0025579319000123

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EP - 718

JO - Mathematika

JF - Mathematika

IS - 3

ER -

EMBEDDING OF THE FREE ABELIAN TOPOLOGICAL GROUP A(X⊕X) INTO A(X)

Abstract

Keywords

All Science Journal Classification (ASJC) codes

Access to Document

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