Homogeneity and \(\pi\)-networks
Let \(B_ 0\) be the class of all zero-dimensional bicompacta of a countable character and let \(B_ 1\) be the class of all linearly ordered continua of a countable character. A space \(X\in B_ 0\) \((X\in B_ 1)\) is said to be h-homogeneous (l-homogeneous) if any two nonempty clopen subsets (nonsingle-point subsegments) of X are homeomorphic (similar). Except for a certain reinforcement of a former result of the author concerning the homogeneity of a space \(X\in B_ 0\) homogeneity properties of products of spaces from the mentioned classes are investigated. For example, if \(\alpha\) is the class of representatives of \(B_ 0\) with respect to the equivalence given by homeomorphism and \(\beta =\{X\in \alpha\); X is homogeneous\(\}\) then the spaces \(\Pi\alpha\) and \(\Pi\beta\) are homeomorphic.
zero-dimensional bicompacta of a countable character
scientific article; zbMATH DE number 4163703