TECHNOLOGY FOCUS - ORGANIC CHEMISTRY - Preferred Structure: The crosslinked structure is of formula (1, 2 or 3).(X)nSi(R23-n)(R1)-SO3H (1)Si(X)n(R3)4-n (2)(R4)n-Si(X3-n)-R5-Si(X3-n)-(R4)n (3)X=-O- coupling or OH group involved in crosslinking;R1=20C or less hydrocarbon group;R2=methyl, ethyl, propyl or phenyl;n in formula (1)=1-3;R3=20C or less alkyl;n in formula (2)=2-4;R5=1-30C atomic-containing molecular chain;R4=methyl, ethyl, propyl, butyl or phenyl;andn in formula (3)=0-2.The crosslinked structure forms a continuous structure of particles, and a proton conduction path is formed at the interval (2) formed by the particles. The metal catalyst particles are supported by the surface of the particles. The three-dimensional crosslinked structure containing silicon-oxygen bond, is a structure of formula (1). The silicon atom having structure of formula (1), is 3% or more. The crosslinked structure having acidic radical contains a mercapto group.Preferred Method: An acidic-radical-containing structure is formed by sol-gel reaction. The mercapto group of the crosslinked structure is oxidized prior to substitution. A mixture of mercapto-group-containing compound having covalent-bonded hydrolysable silyl group and/or silanol group, and a polar controlling-agent is prepared. A film of continuous structure of the particles consisting of a silicon-oxygen crosslinked structure, is formed by condensing hydrolysis and condensation of mixture. The mercapto group in the film is oxidized and set as a sulfonic acid group. The sulfonic acid group is introduced to the surface of the particles. Substitution is then carried out, to obtain a crosslinked structure supporting metal catalyst particles. EXAMPLE - X41-1805 (copolymer of 3-mercapto propyl trimethoxysilane and tetraethoxysilane) (in g) (2.4), tetraethoxysilane (0.6), polyethylene glycol (0.8), triethylamine (2), and water (0.75) were dissolved in tetrahydrofuran (2.7 mL), and stirred at room temperature for 10 minutes. The mixture was allowed to stand in a Petri dish for 3 days at room temperature. The obtained film was heated under 80degreesC humidification for 12 hours. The film was immersed in water, 1N sulfuric acid, and water for 1 hour each. Unreacted substance, triethylamine and polyethylene glycol were extracted from the film. The film was dipped in a mixed solution of peracetic acid (100 ml), and heated at 80degreesC for 1 hour and 200degreesC more for 12 hours. The sheet was removed and dipped in water at 80degreesC thrice, and peracetic acid solution was completely extracted. The sheet was immersed in a platinum compound (Pt(NH3)4(OH)2) aqueous solution at room temperature for 12 hours, and ion substitution was carried out. The sheet was washed and dried, and platinum particles were precipitated. Further washing and drying were carried out to obtain a proton-conduction film with platinum supporting amount of 0.5 mg/1 cm2. A single-cell fuel cell was produced using the obtained proton-conduction film, and evaluated. The maximum-output density was 360 mW/cm2, and the limiting-current density was 1.3 A/cm2. Output reduction was not observed even at a relative humidity of 60%.