Rigidity of products
A metric space \((X,\rho)\) is called \(GA\) if every two of its points can be joined by an arc of finite length. In this case the intrinsic metric can be considered and shown to be equivalent to the original one. A \(GA\) subset \(Y\) of \(X\) is called rigid in \(X\) if every intrinsic isometry of \(Y\) is the restriction of an isometry of \(X\). The author considers \(GA\)- subsets of Euclidean spaces. She presents an example which shows that rigidity of these subsets is not preserved under standard metric products in general. Furthermore additional topological conditions are developed for these subsets which guarantee that rigidity is presented under products.
scientific article; zbMATH DE number 205511