TECHNOLOGY FOCUS - POLYMERS - Preferred Component: The compound containing the ethylenic unsaturated groups is a polyfunctional unsaturated monomer containing (metha)acryloyl groups or vinyl groups in its molecule. The solid polymer electrolyte containing the protonic acid group includes a sulfonated polyarylene having constitutional units of formulae (A) and (B).Y'=-CO-, -SO2-, -SO-, -CONH-, -COO-, -(CF2)i-, or -C(CF3)2;i, j=1-10;Z=a direct bond, -O-, -S-, -(CH2)j-, or -C(CH3)2;Ar=aromatic group having a substituent expressed by -SO3H, -O(CH2)pSO3H, or -O(CF2)pSO3H;p=1-12;m, n=0-10;k=1-4;A, D=a direct bond, -O-, -S-, -CO-, -SO2-, -SO-, -CONH-, -COO-, -(CF2)i-, -(CH2)j-, -CR'2-, cyclohexylidene group, or fluorenylidene group;R'=aliphatic hydrocarbon group, aromatic hydrocarbon group, or halogenated hydrocarbon group;B'=O or S atom;R1-R16=H atom, F atom, alkyl group, partly or fully halogenated alkyl group, allyl group, aryl group, nitro group, or nitrile group;s, t=0-4, andr= greater than or equal to 0.The mixed solution contains a polymerization initiator, which generates a radical by being decomposed by way of photoirradiation. The polymerization initiator is a thermal polymerization initiator. The polymer having a cross-linking structure is obtained by initiating a cross-linking reaction in the compound containing the ethylenic unsaturated groups that constitutes the mixed solution.Preferred Parameter: The sulfonated polyarylene has an ion exchange capacity of 0.3-5 meq/g, and a molecular weight of 10000-1000000. The mixed solution has a viscosity of 1000-20000 mPa.s. EXAMPLE - 3-(2,5-Dichlorobenzoyl) benzenesulfonic acid neopentyl (135.2 g), hydrophobic unit (number average molecular weight=9500) (48.7 g), bis(triphenylphosphine)nickel dichloride (6.71 g), sodium iodide (1.54 g), triphenylphosphine (35.9 g), and zinc (53.7 g) were added into a flask, and purged with dry nitrogen gas. N,N-dimethylacetamide (DMAc) (430 ml) was added into the mixture, the reaction mixture was maintained at 80 degrees C and was stirred for 3 hours, and then the reaction mixture was diluted with DMAc (730 ml), and insoluble matter was filtered. The resulting solution was stirred while heating at 115 degrees C, and then lithium bromide (44 g) was added. The mixture was stirred for 7 hours, and then the reaction liquid was poured into acetone (5 L) to precipitate the product. The precipitate was rinsed with 1 N hydrochloric acid (HCl) and pure water, and then dried to obtain the sulfonated polyarylene (122 g) having weight average molecular weight of 135000. The sulfonated polyarylene (2.00 g) and KAYARAD DPHA(RTM: dipentaerythritol hexaacrylate) (0.20 g) were dissolved in N-methyl-2-pyrrolidone (NMP) (12.50 g) to obtain the mixed solution, which was then applied onto a polyethyleneterephthalate (PET) film by way of cast coating, dried at 120 degrees C for 60 minutes to remove NMP, and a film was formed. The formed film was taken off from the PET film, and set in a metal frame, and then heated at 170 degrees C for 120 minutes for cross-linking reaction. The film thickness of the obtained electrolyte membrane was 40 microns. The membrane exhibited proton conductivity of 0.30 S/cm. It provided a membrane-electrode assembly, which was used in solid polymer electrolyte fuel cell. As evaluation of low temperature startability, the fuel cell was activated 50 times under condition at -30 degrees C, in which the membrane-electrode assembly was evaluated as satisfactory i.e. amount of performance degradation was less than or equal to 20 mV at 0.8 A/cm2. The electrode adhesiveness was 100%; and power generating performance was 0.653 V.