Filter Exhaustiveness and $\Cal F$-$\alpha$-Convergence of Function Sequences

Hüseyin Albayrak, Serpil Pehlivan

In this work, we generalize the concepts of exhaustiveness, $\alpha$-convergence, Cauchy sequence, pointwise convergence and uniform convergence for sequences of functions on metric spaces in terms of filters. We investigate some properties of these new concepts. We also examine the relations between the new concepts and the classical concepts.