Advanced Search

We study several kinds of statistical convergence of sequences of functions with values in semi-uniform spaces. Particularly, we generalize to statistical convergence the classical results of C. Arzelà, Dini and P.S. Alexandroff, as well as their statistical versions studied in [Caserta A., Di Maio G., Kočinac L.D.R., {Statistical convergence in function spaces},. Abstr. Appl. Anal. 2011, Art. ID 420419, 11 pp.] and [Caserta A., Kočinac L.D.R., {On statistical exhaustiveness}, Appl. Math. Lett....

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 $f:X\to Y$ is $\tau$-continuous, then the map $S{P}^{n}f:S{P}^{n}X\to S{P}^{n}Y$ is also $\tau$-continuous. c) We show that the functor $S{P}^n$ preserves the functional tightness and the minimal tightness of compacts. d) Finally, we give some facts and properties on $\tau$-bounded...