On local cross sections in topological abelian groups
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On local cross sections in topological abelian groupsData
2018Cita bibliográfica
Bello, H. J., Chasco, M. J., Domínguez, X., & Stevens, T. C. (2019). On local cross sections in topological abelian groups. Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 113, 2145-2154. https://doi.org/10.1007/s13398-018-0599-4
Resumo
[Abstract:] We introduce the notion of local pseudo-homomorphism between two topological abelian groups. We prove that it is closely related with the widely studied notions of local cross sections and splitting extensions in the category of topological abelian groups. In the final section we present an example of a non-splitting extension of (R, τν ) by R, where τν is a metrizable group topology on R weaker than the usual one. This extension admits a local cross section.
Palabras chave
Local cross section
Extension of topological abelian groups
Local pseudo-homomorphism
Quasi-homomorphism
Weakened
Lie group
Extension of topological abelian groups
Local pseudo-homomorphism
Quasi-homomorphism
Weakened
Lie group
Descrición
Versión aceptada de https://doi.org/10.1007/s13398-018-0599-4
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© Springer-Verlag Italia S.r.l., part of Springer Nature 2018