Forme Equivalente \`a la Condition ${\mathrm{\Delta }}_2$ et Certains r\'esultats de s\'eparations dans les Espaces Modulaires

In this paper, we present an equivalent form of the ${\mathrm{\Delta }}_2$-condition which allow us to redefine the topological vector space structure of a modular spaces using the filter base. We show also the characterization of closed subsets (in the sens of this topology) of a modular spaces which permit us to establish some separation results in modular spaces