Atomicity of mappings
Summary: A mapping \(f:X\to Y\) between continua \(X\) and \(Y\) is said to be atomic at a subcontinuum \(K\) of the domain \(X\) provided that \(f(K)\) is nondegenerate and \(K=f^{-1}(f(K))\). The set of subcontinua at which a given mapping is atomic, considered as a subspace of the hyperspace of all subcontinua of \(X\), is studied. The introduced concept is applied to get new characterizations of atomic and monotone mappings. Some related questions are asked.
scientific article; zbMATH DE number 1230049