We give a necessary and sufficient condition under which gluings of hyperconvex metric spaces along weakly externally hyperconvex subsets are hyperconvex. This leads to a full characterization of hyperconvex gluings of two isometric copies of the same hyperconvex space. Furthermore, we investigate the case of gluings of finite dimensional hyperconvex linear spaces along linear subspaces. For this purpose, we characterize the weakly externally hyperconvex subsets of [Formula: see text] endowed with the maximum norm.
Weakly externally hyperconvex subsets and hyperconvex gluings