On statistically convergent sequences of real numbers

The notion of the statistical convergence of sequences of real numbers was introduced in papers [1] and [5]. In the present paper we shall show that the set of all bounded statistically convergent sequences of real numbers is a nowhere dense subset of the linear normed space m (with the sup-norm) of all bounded sequences of real numbers and the set of all statistically convergent sequences of real numbers is a dense subset of the first Baire category in the Frechet space s. 1