TECHNOLOGY FOCUS - INORGANIC CHEMISTRY - Preferred Method: The nanoporous metal oxide material is obtained by heat treating a fluid raw material composition containing zirconia colloidal particles and/or a zirconium salt solution, and ceria colloidal particles and/or a cerium salt solution without practical coprecipitation after mixing the composition at a shear rate of greater than or equal to1000 seconds -1.Preferred Component: Alumina colloidal particles and/or aluminum salt solution are further contained in the fluid raw material composition.Preferred Parameter: Powder(s) from zirconia powder, ceria powder, or alumina powder, which has average particle size of 0.01-50 microns, is further contained in the nanoporous metal oxide material. When spectra for all metal elements of metal oxides whose content in the nanoporous metal oxide material is greater than or equal to10 at.% are measured by energy dispersive x-ray spectroscopy at measuring points in a region where a sample thickness can be regarded as almost constant using transmission electron microscope with an electron beam diameter of 1.0 nm, and an accelerating voltage of 200 kV, a mean Xm of relative intensity ratio X derived, by converting integrated intensity of fluorescent x-ray peak of each metal element in obtained spectra to relative ratio, and a second moment v2 around the mean Xm satisfy a condition expressed by formula v2/Xm2less than or equal to0.02 (1) or v2/Xm2less than or equal to0.1 (8) for all the metal elements.Xm=mean of relative intensity ratio X and is described by an equation (Xm=(~SX)/N);N=number of measuring points;v2=second moment around the mean Xm, and is described by an equation (v2=(~S(X-Xm)2)/N;v2/Xm2=second moment normalized to the square of the mean Xm.When an equation K value (%)=(x-ray intensity detected from nanoporous metal oxide material)/(x-ray intensity obtained from pure substance) (2) is obtained by an arbitrary line analysis of greater than or equal to0.5 mm for all metal elements of metal oxides whose content is greater than or equal to10 at.% in the nanoporous metal oxide material using x-ray microanalyzer with an electron beam diameter of 1.0 microns and an accelerating voltage of 15 kV, a K value expressed by (2) satisfies a condition expressed by formula (|K-Km|/Km)less than or equal to0.02 (3) for all the metal elements in greater than or equal to65% of measuring points out of total measuring points.K=the K value (%) at each measuring point;Km=mean of K values of all the measuring points, in (3), where a part corresponding to cracks formed in the nanoporous metal oxide material is excluded from the measuring points.When a surface height image of the nanoporous metal oxide material is measured arbitrarily with a tapping mode by a scanning probe microscope using a tip with a curvature radius of 5 nm with an interval of greater than or equal to3 nm and less than 4 nm, a height image H (L) derived as a function of a scan length L total of greater than or equal to2 microns satisfies a condition expressed by formula H(L)less than or equal to20 nm (4) in greater than or equal to80% of measuring points out of total measuring points and a second derivative H"(L) derived from formulae H'(L)=dH/dL=(H(L+DeltaL)-H(L))/DeltaL (5) and H"(L)=d2H/dL2=(H'(L+DeltaL)-H'(L))/DeltaL (6) satisfies a condition expressed by formula H"(L)=-0.05-0.05 nm-1 (7) in less than or equal to60% of measuring points out of total measuring points. In formula (4),H(L)=height image (nm) at each measuring point (scan length=L), where a mean of height images H of all the measuring points is set to zero.In formulae (5) and (6),H(L)=height image (nm) at a measuring point where a scan length is L;H(L+DeltaL)=height image (nm) at a measuring point where a scan length is L+DeltaL;DeltaL=interval (nm) among measuring points;H'(L)=first derivative of a height image H(L);H'(L+DeltaL)=first derivative of height image H(L+DeltaL);H"(L)=second derivative of a height image H(L), where DeltaL is set to 4 nm by linear interpolation among measuring points.When a measuring line is drawn arbitrarily for total of greater than or equal to400 microns on the nanoporous metal oxide material in an electron micrograph of a section of the nanoporous metal oxide material, length ratio of a part where the measuring line intersects with a void portion formed in the nanoporous metal oxide material satisfies a condition that it is less than or equal to10% of total length of the measuring line. EXAMPLE - Aluminum oxide (Al203) colloid, zirconium (Zr) solution, and cerium (Ce) solution were mixed, so that the weight ratio among Al203, zirconium oxide (ZrO2, and cerium oxide CeO2 in the coating to be obtained became Al203:ZrO2:CeO2=35:30:35, and then diluted with methanol to prepare a colloidal solution with a solid concentration of 12 wt.%. Obtained colloidal solution was mixed for 2 minutes at a shear rate of 20000 seconds -1, and then gently mixed (stirring rate of 20 revolutions/minute) for 1 minute to remove air bubbles from the resulting colloidal solution to obtain a coating composition.