Topological and topological linear properties of the Sugeno-Lorentz spaces

The properties of the spaces of Sugeno integrable functions are quite different from those of the ordinary spaces of Lebesgue integrable functions. The purpose of the paper is to further advance our study of the Sugeno-Lorentz spaces, in which the completeness and separability of the spaces were discussed. As a continuation of our previous research, in this paper, some fundamental topological and topological linear properties of the Sugeno-Lorentz spaces are investigated in detail.