NOVELTY - Hydrogen gas formed by electrolysis of pure water in electrolyzer (10) is supplied to hydrogen gas pipe (20a) equipped with a deoxidization catalyst (30a). Heat generated during electrolysis is supplied by a heat-energy feed zone (40) to the deoxidization catalyst.    USE - For producing pure oxygen gas and pure hydrogen gas by electrolysis of water.    ADVANTAGE - Impurities present in hydrogen and oxygen are removed effectively by use of deoxidization catalyst and dehydrogenation catalyst. Pure water temperature is lowered, as heated pure water is circulated to the catalysts. Hence, aggravation of electrolysis is prevented by preventing temperature rise of pure water supplied to the electrolytic cell. Efficiency reduction of ion exchange resin present in the closed circuit is controlled effectively by preventing increase in temperature of pure water supplied to the ion exchange resin. There is no need to use a separate heat source for heating the deoxidization or dehydrogenation catalyst because heat energy produced due to electrolysis is supplied to the catalyst.    DETAILED DESCRIPTION - An electrolytic cell (11) comprises an anode chamber, a cathode chamber and a solid electrolyte film. Pure water is supplied to the cell from a storage tank (12) by supply line (13a). A circulation line (13b) returns the pure water which has not been electrolyzed, from the cell to the storage tank. A closed circuit is formed between the electrolytic cell and the storage tank. Heated pure water is supplied to the deoxidization catalyst from the closed circuit and is returned back to the closed circuit. The pure water is heated during electrolysis. Oxygen gas formed by electrolysis of pure water in the electrolyzer, is supplied to an oxygen gas pipe (20b) equipped with a dehydrogenation catalyst (30b). The heat-energy feed zone supplies heat energy also to the dehydrogenation catalyst. Heated pure water is supplied to the dehydrogenation catalyst from the closed circuit and is returned back to the closed circuit.    An INDEPENDENT CLAIM is also included for pure gas production method which comprises extracting hydrogen, oxygen gas formed during electrolysis by respective hydrogen, oxygen gas pipes equipped with deoxidization catalyst and dehydrogenation catalyst, respectively. Heat energy produced during electrolysis of water is supplied to the deoxidization catalyst and to the dehydrogenation catalyst.    DESCRIPTION OF DRAWING(S) - The figure shows the block diagram of the pure gas production system by electrolysis of water.    Electrolyzer (10)    Electrolytic cell (11)    Storage tank (12)    Supply line (13a)    Circulation line (13b)    Hydrogen gas pipe (20a)    Oxygen gas pipe (20b)    Deoxidization catalyst (30a)    Dehydrogenation catalyst (30b)    Heat-energy feed zone (40)