The present invention prevents the oxidization of a member of carbon fibers and improves the electric connection between the carbon fibers and the member of carbon fibers. In the present invention, a member 5 of carbon fibers 4 includes: a first element selected from the group consisting of IVa group elements and Va group elements; a second element selected from the group consisting of C, Al, Si, Cr, and Zr; and N. Preferably, the first element is Ti. More preferably, the member 5 includes Al or Si and the ratio of Al or Si to Ti is not less than 10 atm % and not more than 30 atm %.