Semistable holomorphic vector bundle ($\mu (F)\le \mu (E)\text{ for every }0\ne F⊊E$)

A positive-rank holomorphic vector bundle on a compact Riemann surface is semistable when every nonzero proper holomorphic subbundle has slope at most its own. Equivalently one tests coherent subsheaves: saturation on a smooth curve preserves rank, increases degree, and gives a subbundle with torsion-free quotient. Strict inequality defines stability, which is stronger.