WE CLAIM:
1. A method of producing a metal oxide fiber, comprising:
a spinning step of spinning a composition containing polymetalloxane and an organic solvent to obtain a thread-like product; and
a firing step of firing the thread-like product obtained in the spinning step at a temperature of 200°C or higher and 2,000°C or lower to obtain a metal oxide fiber;
wherein the polymetalloxane has a repeating structure composed of a metal atom selected from the group consisting of Al, Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn, Ga, Ge, Y, Zr, Nb, Mo, Pd, Ag, In, Sn, Sb, Hf, Ta, W and Bi, and an oxygen atom;
wherein the weight average molecular weight of the polymetalloxane is 20,000 or more and 2,000,000 or less.
2. The method of producing a metal oxide fiber according to claim 1, wherein the viscosity of the composition at 25°C is 10 P or more and 50,000 P or less.
3. The method of producing a metal oxide fiber according to claim 1 or 2, wherein the average fiber diameter is 0.01 urn or more and 1,000 urn or less.
4. The method of producing a metal oxide fiber according to any one of claims 1 to 3,
wherein the composition contains an organic polymer; and
wherein the content of the organic polymer in the composition is 1% by
weight or less relative to the weight of the polymetalloxane contained in the
composition.
5. The method of producing a metal oxide fiber according to any one of claims 1
to 4, wherein the composition does not contain any of an alkali metal and an alkaline

earth metal.
6. The method of producing a metal oxide fiber according to any one of claims 1 to 5, wherein the composition does not contain any of silicic acid, a silicate salt, silica gel, a silicate ester, boric acid, a borate salt, and a borate ester.
7. The method of producing a metal oxide fiber according to any one of claims 1 to 6, wherein the polymetalloxane has at least one of a structural unit represented by the following general formula (1) and a structural unit represented by the following general formula (2):
wherein in the general formula (1) and the general formula (2),
1 Q
R and R are arbitrarily selected from a hydrogen atom, an alkyl group having 1 to 12 carbon atoms, or a group having a metalloxane bond;
R is arbitrarily selected from a hydroxy group, an alkyl group having 1 to 12 carbon atoms, an alicyclic alkyl group having 5 to 12 carbon atoms, an alkoxy group having 1 to 12 carbon atoms, an aromatic group having 6 to 30 carbon atoms, a phenoxy group having 6 to 30 carbon atoms, and a naphthoxy group having 10 to 30 carbon atoms;

when a plurality of R , R , and R exist, they are optionally the same or different;
R4 is arbitrarily selected from a hydroxy group, an alkyl group having 1 to 12 carbon atoms, an alicyclic alkyl group having 5 to 12 carbon atoms, an alkoxy group having 1 to 12 carbon atoms, an aromatic group having 6 to 30 carbon atoms, and a group having a siloxane bond;
M represents a metal atom selected from the group consisting of Al, Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn, Ga, Ge, Y, Zr, Nb, Mo, Pd, Ag, In, Sn, Sb, Hf, Ta, W, and Bi;
m is an integer indicating the valence of the metal atom M;
a is an integer of 0 to (m-2); and
b is an integer of 1 to (m-2).
8. The method of producing a metal oxide fiber according to claim 7,
wherein the polymetalloxane has at least a structural unit represented by the
general formula (1); and
wherein at least one of R in the general formula (1) is a hydroxy group.
9. The method of producing a metal oxide fiber according to claim 7 or 8, wherein the polymetalloxane has at least a structural unit represented by the general formula (2).
10. The method of producing a metal oxide fiber according to any one of claims 7 to 9, wherein the metal atom M in the polymetalloxane comprises at least one metal atoms selected from the group consisting of Al, Ti, Zr, and Sn.
11. The method of producing a metal oxide fiber according to any one of claims 7

to 10,
wherein the metal atom M in the polymetalloxane comprises Ti; and wherein the ratio of Ti in the entire metal atom M in the metal oxide fiber is
in a range of 5 mol% or more and 100 mol% or less.
12. The method of producing a metal oxide fiber according to any one of claims 7
to 10,
wherein the metal atom M in the polymetalloxane comprises Zr; and wherein the ratio of Zr in the entire metal atom M in the metal oxide fiber is in a range of 5 mol% or more and 100 mol% or less.
13. The method of producing a metal oxide fiber according to any one of claims 1
to 12, wherein the spinning step is a step of spinning the composition by a dry
spinning method or an electro-spinning method.
14. A metal oxide fiber, comprising
Si, and
at least one metal atom selected from the group consisting of Al, Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn, Ga, Ge, Y, Zr, Nb, Mo, Pd, Ag, In, Sn, Sb, Hf, Ta, W, and Bi;
wherein the content of the SiC>2 component in the metal oxide is 0.5% by weight or less.
15. The metal oxide fiber according to claim 14, wherein the average fiber diameter is 0.01 urn or more and 1,000 urn or less.
16. The metal oxide fiber according to claim 14 or 15, wherein the metal atom in

the metal oxide comprises at least one metal atom selected from the group consisting of Al, Ti, Zr, and Sn.
17. The metal oxide fiber according to claim 14 or 15,
wherein the metal atom in the metal oxide comprises Ti; and
wherein the ratio of Ti in the entire contained metal atom is in a range of 5 mol% or more and 100 mol% or less.
18. The metal oxide fiber according to claim 14 or 15,
wherein the metal atom in the metal oxide comprises Zr; and
wherein the ratio of Zr in the entire contained metal atom is in a range of 5 mol% or more and 100 mol% or less.
19. The metal oxide fiber according to claim 14 or 15, wherein the metal atom in
the metal oxide comprises two or more metal atoms selected from the group
consisting of Al, Ti, Zr, and Sn.