TECHNOLOGY FOCUS - POLYMERS - Preferred Components: The hollow fiber comprises a dense layer including picopores at a surface portion. The dense layer has a 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 hydroxy, thiol or amine 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 polyimide is polyimide of formula (1a)-(4a), polyimide copolymers of formula (5a)-(8a), or their copolymers or blends. The mole ratio of each repeating unit (1a) to (4a) in the polyimide copolymers or a m:l mole ratio in (5a) to (8a) is 0.1:9.9-9.9:0.1. The thermally rearranged polymer comprises a polymer of formula (19a) to (32a), or their copolymers. The polyimide has a weight average molecular weight (Mw) of 10000-200000. The polyimide (1a)-(8a) is obtained from imidization of polyamic acid of formula (33a)-(40a).Ar1 = aromatic group comprising quadrivalent 6-24C arylene group or quadrivalent 4-24C heterocyclic group (both optionally substituted), 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;p, q = 1-10;Ar1a, Ar2 = aromatic group comprising divalent 6-24C arylene group or divalent 4-24C heterocyclic group (both optionally substituted), 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;Q = O, S, S(=O)2, C(=O), C(CH3)2 or C(CF3)2 (all preferred), CH(OH), Si(CH3)2, (CH2)p, (CF2)q, C(=O)NH, C(CH3)(CF3), or phenylene group (optionally substituted by 1-6C (halo)alkyl group), where Q is linked with aromatic groups with m-m, m-p, p-m, or p-p positions;Y1 = OH, SH or NH2;Y2a = O or S;n = 20-200; andm, l = 10-400.Where Ar1, Ar2 and Ar1a are preferably phenyl, naphthyl, anthracenyl, perylenyl, biphenyl, terphenyl, diphenyl ether, diphenyl thioether, diphenyl methane, diphenyl difluoromethane, diphenyl ketone, 2,2-diphenyl propane, 2,2-diphenyl hexafluoropropane, diphenyl sulfonyl, diphenyl methanol, diphenyl dimethyl 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. Preferred Composition: The dope solution composition comprises 10-45 wt.% of the polyimide, 25-70 wt.% of the organic solvent, and 2-30 wt.% of the additive. The dope solution composition has a viscosity of 2-200 Pa-s. Preferred Process: The imidization comprises chemical imidization or solution-thermal imidization. The chemical imidization is performed at 20-180 degrees C for 4-24 hours. The chemical imidization further comprises protecting an ortho-positioned functional group of polyamic acid with a protecting group before imidization, and removing the protecting group after imidization. The solution-thermal imidization is performed at 100-180 degrees C for 2-30 hours in a solution. The solution-thermal imidization further comprises protecting an ortho-positioned functional group of polyamic acid with a protecting group before imidization, and removing the protecting group after imidization. The solution-thermal imidization is performed using an azeotropic mixture. The heat treatment is performed by increasing a temperature at 10-30 degrees C/minute up to 400-550 degrees C, and then maintaining the temperature for 1 minute to 1 hour under an inert atmosphere. EXAMPLE - 2,2-Bis(3-amino-4-hydroxyphenyl) hexafluoropropane (36.6 g) was added to a nitrogen-purged reactor and N-methylpyrrolidone (NMP) solvent was added. The reactor was placed in an oil bath to constantly maintain the reaction temperature at -15 degrees C. 4,4'-(Hexafluoroisopropylidene)diphthalic anhydride (44.4 g) was added to the solution and allowed to react for 4 hours to prepare a pale yellow viscous polyhydroxyamic acid solution. Toluene (300 ml) was added to the polyhydroxyamic acid solution. While the temperature of the reactor was increasing up to 150 degrees C, polyhydroxyimide was obtained by performing reaction for 12 hours through thermally solution imidization using azeotropic mixture. The resulting polyimide was added to NMP (243 g) and 10 wt.% of ethanol was added to prepare a homogeneous dope solution composition. The dope solution composition was defoamed at ambient temperature under reduced pressure for 24 hours. The resulting solution was allowed to stand at 25 degrees C and was then spun through a double-ring nozzle. 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 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 prepare a hollow fiber thermally rearranged into polybenzoxazole compound of formula (51a).