TECHNOLOGY FOCUS - POLYMERS - Preferred Composition: The dope solution composition comprises: polyimide (10-45 wt.%), organic solvent (25-70 wt.%) and additive (5-40 wt.%). The dope solution composition has a viscosity of 2-200 Pa-s. Preferred Method: The heat treatment is performed after imidization by increasing a temperature at 10-30 degrees C per minute up to 400-550 degrees C, and then maintaining the temperature for 1 minute to 1 hour under an inert atmosphere. Preferred Components: The hollow fiber comprises a dense layer including picopores at a surface portion. The dense layer has structure, where the number of the picopores increases as near to the surface of the hollow fiber. The three dimensional network structure, where at least two picopores are three-dimensionally connected, comprises an hourglass shaped structure forming a narrow valley at connection parts. The ortho-positioned functional group comprises hydroxyl, thiol or amino group. The polymer has a fractional free volume (FFV) of 0.15-0.40. The polymer has interplanar distance (d-spacing) of 580-800 pm measured by X-ray diffraction (XRD). The polymer comprises picopores, and the picopores has a full width at half maximum (FWHM) of 10-40 pm measured by positron annihilation lifetime spectroscopy (PALS). The polymer has a BET (Brunauer Emmett Teller) surface area of 100-1000 m2/g. The polyamic acid is: polyamic acids of formulae (a)-(d); the polyamic acid copolymers of formulae (e)-(h); or their copolymers or blends. The polymer comprises a polymer compounds of formulae (19)-(32). The polyamic acid has a weight average molecular weight of 10000-200000. The thermally rearranged polymer comprises a polymer comprising (19)-(32), or their copolymers. The polyimide hollow fiber comprises polyimide compound of formulae (33)-(40), their copolymers or their blends. The molar ratio of each repeating unit in (a)-(d) in the polyamic acid copolymers or an m:1 mole ratio in (e)-(h) is 0.1:9.9-9.9:0.1. The ortho-positioned functional group comprises hydroxyl, thiol or amino groups.Ar1 = aromatic group comprising optionally substituted quadrivalent 6-24C-arylene or optionally substituted quadrivalent 4-24C-heterocyclic, where the aromatic group is present singularly, at least two aromatic groups are fused to form a condensed cycle, or at least two aromatic groups are linked by single bond or a functional group comprising O, S, C(=O), S(=O)2, Si(CH3)2, (CH2)p, (CF2)q, C(CH3)2, C(CF3)2 or C(=O)NH and Ar1 is preferably benzene-, naphthalene-, phenanthrene-, perylene-, biphenyl-, triphenyl-, biphenyl ketone-, phenylsulfanylbenzene-, benzylbenzene-, (difluoro(phenyl)methyl)benzene-, (1-methyl-1-phenyl-ethyl)benzene-, (2,2,2-trifluoro-1-phenyl-1-(trifluoromethyl)ethyl)benzene-, benzenesulfonylbenzene-, diphenyl-methanol-, dimethyl-diphenyl-silane-, N-phenyl-benzamide-, 1,4-diphenoxy-benzene-, (4-benzoyl-phenyl)-phenyl-methanone-, 1-phenoxy-4-(2,2,2-trifluoro-1-(4-phenoxyphenyl)-1-(trifluoromethyl)ethyl)benzene-, thiophene- or pyrazine-group;Ar1a, Ar2 = aromatic group comprising optionally substituted divalent 6-24C-arylene or optionally substituted divalent 4-24C-heterocyclic, where the aromatic group is present singularly, at least two aromatic groups are fused to form a condensed cycle, or at least two aromatic groups are linked by single bond or a functional group comprising O, S, C(=O), S(=O)2, Si(CH3)2, (CH2)p, (CF2)q, C(CH3)2, C(CF3)2 or C(=O)NH, and Ar1a, Ar2 are preferably benzene-, naphthalene-, phenanthrene-, perylene-, biphenyl-, triphenyl-, phenoxybenzene-, phenylsulfanylbenzene-, benzylbenzene-, (difluoro(phenyl)methyl)benzene-, biphenyl ketone-, (2,2,2-trifluoro-1-phenyl-1-(trifluoromethyl)ethyl)benzene-, (1-methyl-1-phenyl-ethyl)benzene-, benzenesulfonylbenzene-, diphenyl-methanol-, dimethyl-diphenyl-silane-, N-phenyl-benzamide-, 1,4-diphenoxy-benzene-, (4-benzoylphenyl)-phenyl-methanone-, 1,4-diphenoxybenzene-, 1-phenoxy-4-(2,2,2-trifluoro-1-(4-phenoxyphenyl)-1-(trifluoromethyl)ethyl)benzene-, thiophene- or pyrazine-group;Q = O, S, S(=O)2, C(CH3)2 or C(=O) (all preferred), CH(OH), Si(CH3)2, (CH2)p, (CF2)q, C(CF3)2, C(=O)NH, C(CH3)(CF3), or optionally substituted phenylene group (where the substituted phenylene group is a phenylene group substituted with 1-6C-alkyl or 1-6C-haloalkyl, and the Q is linked with aromatic groups with m-m, m-p, p-m or p-p positions);p, q = 1-10;Y1 = OH, SH or NH2;n = 20-200; andl, m = 10-400. EXAMPLE - 2,2-Bis(3-amino-4-hydroxyphenyl) hexafluoropropane (36.6 g) and 4,4'-(hexafluoroisoproylidene) diphthalic anhydride (44.4 g) were added into (70 wt.%) of N-methylpyrrolidone (189 g) and then reacted at 15 degrees C for 4 hours to obtain a pale yellow viscous polyamic acid. The resulting polyamic acid was added to tetrahydrofuran (5 wt.%) as an additive without removal of the solvent to prepare a homogeneous dope solution composition for forming a hollow fiber. The dope solution composition was defoamed at ambient temperature under reduced pressure for 24 hours, and foreign materials were removed. Subsequently, the resulting solution was allowed to stand at 25 degrees C and was then spun through a double-ring nozzle. At this time, distilled water was used as an internal coagulating solution and an air gap was set at 50 cm. The spun hollow fiber was coagulated in a coagulation bath including water at 25 degrees C and was then wound at a rate of 20 m/minute. The resulting hollow fiber was washed, air-dried at ambient temperature for 3 days. Then the dried hollow fiber was imidized at 300 degrees C for 1 hour, and then heat-treated under an inert atmosphere at 500 degrees C for 10 minutes at a heating rate of 15 degrees C/minute using heating furnace to obtain a hollow fiber thermally rearranged into polybenzoxazole compound of formula (51).