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On local cross sections in topological abelian groups. (English) Zbl 1420.22002
Summary: 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 $$(\mathbb{R},\tau _\nu )$$ by $$\mathbb{R}$$, where $$\tau _\nu$$ is a metrizable group topology on $$\mathbb{R}$$ weaker than the usual one. This extension admits a local cross section.
##### MSC:
 22A05 Structure of general topological groups 54H11 Topological groups (topological aspects) 22E41 Continuous cohomology of Lie groups
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