Reflexive extended locally convex spaces
The authors continue their investigation of extended locally convex spaces (elcs) in the sense of \textit{D.~Salas} and \textit{S.~Tapia-García} [Topology Appl. 210, 317--354 (2016; Zbl 1359.46003)]. Here, they use the topology \(\tau_{ucb}\) of uniform convergence on bounded subsets of an elcs \((X,\tau)\) to explore its reflexivity property. In particular, they show that an elcs is (semi) reflexive if and only if its open subspaces are (semi) reflexive. Moreover, it is shown that reflexivity of extended normed spaces is a three-space property.
scientific article; zbMATH DE number 7915149