A support member is comprised of a carrier which holds a volatile component. The carrier is comprised of a three-dimensional knitted fabric. The three-dimensional knitted fabric is comprised of a first knitted fabric layer, a second knitted fabric layer, and connecting yarns between these layers. The connecting yarns connect the first knitted fabric layer with the second knitted fabric layer. At least one knitted fabric layer has a mesh-like structure. A plurality of connecting yarns extend from each stitch of the first knitted fabric layer to each stitch of the second knitted fabric layer and connect each other's stitch. The volatile component is impregnated in the carrier or adhered to the carrier, so that the volatile component is held by the carrier.