Low leachable fibers and fiber structure

A method of filtering water or air, the method comprising:

• passing water or air through a filter comprising a fiber structure made from a fiber comprising a cyclic olefin-based resin as the only resin in the fiber,
• wherein the cyclic-based resin is an addition copolymer of a cyclic olefin of formula (I) and an alpha-olefin or a hydrogenated product thereof:
• wherein
• R1-R12 are each independently hydrogen, halogen or hydrocarbon;
• R9, R10, R11 and R12 may optionally form a divalent hydrocarbon group or a cycle;
• n is 0 or a positive integer and, when n is 2 or higher, R5-R8 may be the same or different within respective repeat units;
• wherein
• the fiber is obtained by a process of extruding, spinning, cooling and winding the olefin-based resin, wherein the spinning is conducted at or above a glass transition temperature of the olefin-based resin and at or below 250° C. above the glass transition temperature while supplying inert gas and removing oxygen gas,
• a single filament fineness of the fiber is from 0.1 to 10 dtex, and
• a difference between the temperature at which the olefin-based resin loses five percent by weight and the fiber obtained by spinning the olefin-based resin in the presence of an inert gas loses five percent by weight is 20 degrees Celsius or lower as measured thermogravimetrically according to JIS K 7120.