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

Krupski Mikołaj | Zendy; Leiderman Arkady | Zendy; Morris Sidney | Zendy

AI Assistant Blog Pricing

Home ZAIA Blog

Premium

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

Author(s) -

Krupski Mikołaj,

Leiderman Arkady,

Morris Sidney

Publication year - 2019

Publication title -

mathematika

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.955

H-Index - 29

eISSN - 2041-7942

pISSN - 0025-5793

DOI - 10.1112/s0025579319000123

Subject(s) - mathematics , embedding , abelian group , topological group , separable space , group (periodic table) , metrization theorem , free group , topological ring , g module , pure mathematics , topology (electrical circuits) , topological space , discrete mathematics , elementary abelian group , combinatorics , topological vector space , mathematical analysis , chemistry , organic chemistry , artificial intelligence , computer science

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 ) .

This content is not available in your region!

Continue researching here.

Having issues? You can contact us here

Accelerating Research