To obtain a titanium dioxide-fixed three-dimensional filament spaced structure and a catalytic material fixed in a material such as a porous zeolite, and to provide a device for the oxidative decomposition of an object such as air, water, environmental soil, an oil film, an exhaust gas or the like and a basic system construction.

A thermoplastic raw material is extruded in the form of a molten filament from a plurality of nozzles with different filament diameters such as large, medium and small perforated in a die, and the filaments are mutually fused together by irregularly meandering them on the level of a cooling liquid and making the filaments come into contact with the surfaces of the other adjacent filaments prior to the setting of the filaments. In addition, the filaments are set to a fixed form such as cylindrical, flat platelike or boxlike using a form-setting frame while being arranged into irregular three-dimensional spaces, and then are taken up by a take-up device at a specified take-up rate. Thus, the three-dimensional filament spaced structure 1 is obtained which is of a three-dimensional reticular shape such as cylindrical, flat platelike or boxlike of the filaments set by cooling. A powdery titanium dioxide is fixed on the linear surface constituting the structure 1 by the help of an adhesive.