Spaces close to \({\mathbb{R}}^ n\) (Q2640934)

Only finite-dimensional locally compact metric spaces with a countable base are considered. By the theorem of Brouwer each n-dimensional closed subset F of \(R^ n\) has nonempty interior Int F, which also satisfies the following conditions: (a) Int F contains the cube \(I^ n\). (b) Int F contains a set V open in \(R^ n\) and homeomorphic to \(R^ n\). - The author defines a class of spaces with a property similar to property (b), and with the help of this class, using a modification of property (a), he gives a characterization of the open sets of \(R^ n\).