dyeable and dyed filaments have a core and a sheath which entirely surrounds the core . the core is formed of a core polymer which is susceptible to dyeing by a dye bath chemical , while the sheath is formed of a sheath polymer which is resistant to dyeing by the dye bath chemical . when the filament is brought into contact with a dye bath containing the dye chemical , the dye chemical in the dye bath will physically diffuse or migrate through the sheath polymer to cause the core polymer to be dyed a color of the dye bath chemical , while the sheath polymer is substantially undyed thereby .