Bello, Hugo J.Chasco, MJDomínguez, XabierStevens, T. Christine2024-02-012024-02-012018Bello, 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/s13398-018-0599-4http://hdl.handle.net/2183/35331Versión aceptada de https://doi.org/10.1007/s13398-018-0599-4[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.eng© Springer-Verlag Italia S.r.l., part of Springer Nature 2018Local cross sectionExtension of topological abelian groupsLocal pseudo-homomorphismQuasi-homomorphismWeakenedLie groupjournal articleopen access10.1007/s13398-018-0599-4