On continuity of group-valued mappings with respect to Chabauty topology

Abstract Let 𝐺 be a locally compact group and let <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mi mathvariant="script">S</m:mi> <m:mo>⁢</m:mo> <m:mi mathvariant="script">U</m:mi> <m:mo>⁢</m:mo> <m:mi mathvariant="script">B</m:mi> <m:mo>⁢</m:mo> <m:mrow> <m:mo stretchy="false">(</m:mo> <m:mi>G</m:mi> <m:mo stretchy="false">)</m:mo> </m:mrow> </m:mrow> </m:math> \mathcal{SUB}(G) be the set of closed subgroups of 𝐺 equipped with the Chabauty topology. In this paper, we establ