ON THE METRIC AND THE TOPOLOGICAL PROPERTIES OF THE CONVERGENCE FIELD OF REGULAR MATRIX TRANSFORMATIONS

It has been shown by some researchers that the convergence field of regular matrix transformation is a very porous set in the spaceof all sequence of real or complex numbers while in [11 ], it have been proven to be σ-porous set in the linear metric space endowed with Fréchet metric. Also, the usefulness of the well-known theorem on discontinuity points of function of the first bare class has been presented. Thus in this paper, we proved that the convergence field of a various matrix transformation is a metric space as well as a topological space. Further, we have shown that the space is normal and first countable; compact and complete and have unique fix point.