A note on functional tightness and minitightness of space of the $G$-permutation degree

The current topic is devoted to the investigation of behavior of the minimal tightness and functional tightness of topological spaces under the influence of functor of permutation degree. It is proved that the functor preserves the functional tightness and the minimal tightness of compacts. We introduce the notion of $\tau$-open sets and investigate some basic properties of them.