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Statistical convergence of sequences of functions with values in semi-uniform spaces

Dimitrios N. Georgiou;  Athanasios C. Megaritis;  Selma Özçağ — 2018

Commentationes Mathematicae Universitatis Carolinae

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....

A study of universal elements in classes of bases of topological spaces

Dimitris N. Georgiou;  Athanasios C. Megaritis;  Inderasan Naidoo;  Fotini Sereti — 2021

Commentationes Mathematicae Universitatis Carolinae

The universality problem focuses on finding universal spaces in classes of topological spaces. Moreover, in “Universal spaces and mappings” by S. D. Iliadis (2005), an important method of constructing such universal elements in classes of spaces is introduced and explained in details. Simultaneously, in “A topological dimension greater than or equal to the classical covering dimension” by D. N. Georgiou, A. C. Megaritis and F. Sereti (2017), new topological dimension is introduced and studied, which...

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