A porous, filamentary mat has a plurality of layers that are in intimate face-to-face relation and that have portions of the confronting faces thereof bonded together to enable those layers to constitute a unitary, porous, filamentary mat. Each of the layers has a plurality of elongated filaments of thermoplastic material; and each of those filaments is arranged in an essentially horizontal attitude and is longer than the mat. Each of those filaments has a number of bends therein which cause portions of each filament to cross and to engage other portions of that filament; and those bends also cause portions of each filament to cross and to engage portions of one or more adjacent filaments. The crossing portions of each filament, and the crossing portions of adjacent filaments, are bonded together by initial thermal bonds that are subsequently enhanced; as by pressing together the adjacent crossing portions of the various filaments of the mat while they are in a tacky state, by applying additional heat to the initially-thermally-bonded filaments of the mat to cause the initial thermal bonds to form longer and deeper bond, or by applying both heat and pressure to those initial thermal bonds.