The topological sensitivity with respect to Furstenberg families (Q782125)

Summary: In this work, a dynamical system \((X, f)\) means that \(X\) is a topological space and \(f:X\longrightarrow X\) is a continuous map. The aim of the article is to introduce the conceptions of topological sensitivity with respect to Furstenberg families, \(n\)-topological sensitivity, and multisensitivity and present some of their basic features and sufficient conditions for a dynamical system to possess some sensitivities. Actually, it is proved that every topologically ergodic but nonminimal system is syndetically sensitive and a weakly mixing system is \(n\)-thickly topologically sensitive and multisensitive under the assumption that \(X\) admits some separability.