TECHNOLOGY FOCUS - POLYMERS - Preferred Film: A mixture of monomer which has an epoxy group or oxetanyl group-containing compound having a portion for ion exchange group introduction, or the mixture along with a hardener having portion for ion exchange group introduction, is filled in the pores of porous base material. The monomer is polymerized and an ion exchange group is introduced into the polymer. Polymerization of monomer is performed at temperature of 150 degrees C or less or by actinic ray irradiation. The porous base material consists of a polyolefin.Preferred Polymer: The cross-linked polymer having epoxy group-containing compound as structural component is obtained using imidazole derivative as polymerization catalyst. The polymer having oxetanyl group-containing compound is obtained using photoacid generator as polymerization catalyst.    TECHNOLOGY FOCUS - ORGANIC CHEMISTRY - Preferred Compound: At least a portion of the epoxy group or oxetanyl group-containing has structure of formula (I).A = epoxy group (i) or oxetanyl group (ii) having an oxygen atom;X = hydrogen or methyl;Y = hydrogen, methyl or ethyl;at least one of R = hydrogen and others are hydrogen or functional group, where R is bonded to benzene directly or through another atom; andn = 1-5. EXAMPLE - A cross-linked polyethylene film of 40% porosity and average pore size 0.1 micron was used as porous base material. The material was immersed in polymer precursor liquid which contained 2-ethyl-4-methyl imidazole (0.6 g), phenyl glycidyl ether (4.5 g) and ethylene glycol diglycidyl ether (3.4). The material was removed from the liquid and left in an oven heated at 120 degrees C for 2 hours. The polymer precursor inside the pore was polymerized. The film was then dipped in 1,2-dichloroethane (30 ml) and cooled at 1 degree C in ice bath. 71 ml of 1,2-dichloroethane solution of chlorosulfonic acid diluted to 1 volume% was dropped (over 10 minutes) into the container in which the film was dipped. Stirring was continued for 20 minutes. The film was taken out, washed and air dried. The film was then immersed in 1 N hydrochloric acid for 2 hours and washed using distilled water and dried. The obtained electrolyte film had ion exchange capacity of 1.1 meq/g, proton conductivity of 62 nS/cm, methanol permeability of 0.08 (m2.hour/micron.kg), and excellent durability.