TECHNOLOGY FOCUS - INORGANIC CHEMISTRY - Preferred Source: The proton source is phosphoric acid, hypophosphoric acid, phosphoric acid ester, phosphorus acid ester, tungsto phosphoric acid and/or tungsten peroxo complex.    TECHNOLOGY FOCUS - POLYMERS - Preferred Method: The cross-linked surface is preferably obtained by sol-gel reaction using precursors of formula (1) and (2).R3-R6 = hydrogen atom or substituent;a = mol composition ratio of repeating unit;X1, X2 = same as X, R3, R4 and/or X1 is of formula:-M1(Y1)jZ1k-j;b = 50-100 mol%;p, s = 1-5;M1 = same as M;Y1 = same as Y;Z1 = same as Z;k = number of Y1 and Z1 substituted on M1; andj = 1-k. EXAMPLE - Peroxide di-t-butyl (1 ml) was added to triethoxy vinyl silane (in g) (35) and polymerized in nitrogen atmosphere at 140degreesC for 2 hours, to obtain precursor (A) (33) of formula (1-1). Glycidyl oxypropyl trimethoxysilane (2.4) was dissolved in methylene-chloride (30 ml). Trifluoro boron ether complex (0.13 ml) was added as heat-reflux to the obtained solution. The solution was heat-refluxed for 2 hours, and the solvent was distilled under reduced pressure, to obtain precursor (B) of formula (1-10). Triethoxy vinyl silane (19) and N-vinyl-pyrrolidone (11.1), were dissolved in ethyl acetate (25 ml). V-601 (RTM) (0.15) was added as radical initiator to the obtained solution. The obtained solution was heat-refluxed for 10 hours and polymerized. Hexane was added to the obtained reaction solution, and supernatant liquid of the reaction solution was decanted. The obtained reaction product was dried, to obtain precursor (C) of formula (2-1). Precursor (A) (1) and precursor (B) (1), were dissolved in ethanol (6 ml). 1.6% of hydrochloric acid aqueous solution (0.52 ml) was added to the obtained solution at 25degreesC. Precursor (C) (0.4) was added and stirred at 25degreesC for 20 minutes. Phosphoric acid ethanol solution obtained by dissolving phosphoric acid (0.92) in ethanol, was dropped to the obtained solution. The obtained solution was applied on a Teflon sheet. The sheet was heated at 50degreesC for 2 hours. The heated sheet was left at room temperature for 2 hours. The left sheet was further heated at 120degreesC for 3 hours, to obtain a colorless and transparent sheet having thickness of 230 micrometers. The sheet had ionic conductivity of 0.76 S/cm and excellent flexibility. The obtained sheet was used an catalyst electrode joining film. The catalyst electrode joining film was used in a fuel cell. The fuel cell had stable voltage.