Abstract: We study the behavior of the minimal tightness and functional tightness of topological spaces under the influence of the functor of the permutation degree. Analytically: a) We introduce the notion of \tau-open sets and investigate some basic properties of them. b) We prove that if the map f\colon X\rightarrow Y is \tau-continuous, then the map SP^{n}f\colon SP^n X \rightarrow SP^n Y is also \tau-continuous. c) We show that the functor SP^n preserves the functional tightness and the minimal tightness of compacts. d) Finally, we give some facts and properties on \tau-bounded spaces. More precisely, we prove that the functor of permutation degree SP^n preserves the property of being \tau-bounded.
Keywords: \tau-open set; \tau-bounded space; functional tightness; minimal tightness
DOI: DOI 10.14712/1213-7243.2023.019
AMS Subject Classification: 54C05 54B20