TECHNOLOGY FOCUS - INORGANIC CHEMISTRY - Preferred Components: The cross-linker is an inorganic cross-linker. The thickness of the first ceramic fraction layer is less than 100 nm. The second particle fraction contains a particle with an average particle size of 0.2-5 mu m, and exhibits a Brunauer-Emmett-Teller surface of less than 5 m2/g. The amount of the first- and second fraction is 10-80 parts by weight and 20-90 parts by weight, respectively. The first fraction particle exhibits an average primary particle size of 30-60 nm. The particles of the second fraction and first ceramic fraction are from aluminum oxide particles and silicon oxide, respectively. The process gas used in the plasma treatment is nitrogen, oxygen, air, argon (all preferred), helium, carbon dioxide, carbon monoxide, ozone, silane, alkane, fluoroalkane and/or fluoroalkene. (A) exhibits a polymer sol of silicon compound. The parts by weight of the suspended particle fraction correspond to 1.5-150 times of the used first fraction from the sol. The amount of a fraction with: an average primary particle size of 10-199 nm is 5-50 parts by weight, and an average primary particle size of 200 nm to 5 mu m is 30-94 parts by weight.    TECHNOLOGY FOCUS - ORGANIC CHEMISTRY - Preferred Components: The adhesive agent used during heating process is 3-aminopropyltriethoxysilane or 3-glycidyloxytrimethoxysilane. The adhesive agent used during UV-radiation is methacryloxypropyltrimethoxysilane.    TECHNOLOGY FOCUS - POLYMERS - Preferred Components: The first ceramic fraction exhibits an average particle size of less than 20 nm, and prepared by a particular sol, preferably polymer sol. The polymer fleece is from polymer fibers of polyethylene, polyacrylonitrile, polypropylene, polyamide and/or polyester. (I) can be bent down to a radius of 5 mm, and emerges without any fault. Preferred Process: A radio frequency plasma, cyclotron resonance frequency plasma or microwave plasma is used for the plasma treatment. The plasma power used in the plasma treatment is 10-1000 W. The distance between nozzle and polymer fleece, for the plasma treatment, is 0.1-300 mm. The plasma treatment takes place in a substrate speed of 60-0.002 m/minute. The sol is obtained by the hydrolysis of a precursor compound of aluminum, zirconium, titanium, barium or silicon with water or acid. The treatment with UV-radiation results before or after the heating process. The heating process takes place at 50-350 degrees C. The heating of the polymer fleece, preferably from polyester or polyamide takes place at 200-220 degrees C for 0.5-10 minutes, or 130-180 degrees C for 0.5-10 minutes, respectively. EXAMPLE - Water (130 g), ethanol (15 g), 5 wt.% of aqueous nitric acid solution, tetraethoxy silane (10 g), Dynasylan (RTM: 3-Aminopropyltriethoxysilane) (10 g) and Dynasylan (RTM: 3-Glycidyloxypropyltrimethoxysilane) (10 g) were mixed by stirring. Further Martoxid MZS-1 (RTM: Aluminum oxide) and Martoxid MZS-3 (RTM: Aluminum oxide) (125 g) were suspended on the above mixture and homogenized for at least 24 hours to obtain a coating composition. A polyamide fleece with a width of 55 cm, a thickness of approximately 100 mu m and surface weight of about 30 g/m2 was passed continuously in to the plasma nozzle for about 50 minutes and plasma treated under oxygen atmosphere. The coating composition was coated on the polyamide fleece at 150 degrees C and at a speed of 30 minutes/hour to obtain the ceramic membrane with an average pore value of 450 nm.