A switching device with effective cooling of outflowing gases includes: an arc extinguishing chamber; an orifice for outflow of the gases from the arc extinguishing chamber; and a multilayer wire cloth or fabric having at least a first wire layer and a second wire layer. The first wire layer and the second wire layer have a respective cloth or fabric structure including respective warp yarns and weft yarns. The first and second wire layers are disposed in a stacked configuration in the orifice such that a weaving direction of the warp yarns of the first wire layer is rotated by an angle in relation to a weaving direction of the warp yarns of the second wire layer, and a weaving direction of the weft yarns of the first wire layer is rotated by an angle in relation to a weaving direction of the weft yarns of the second wire layer.