= Quotient operator
{title2=$B_Y(0,c)\subseteq T(B_X(0,1))$}
A quotient operator is a <surjective> <bounded linear operator> that is an <open map>. It is equivalent to requiring a ball about zero in the <image> of the open unit ball. Translation and scaling then prove being an <open map> at every point. For a <Banach space> domain, a <bounded linear operator> is a quotient operator exactly when its <Banach-space adjoint> is an <isomorphic embedding>: a lower bound on the adjoint gives approximate ball-surjectivity by <Hahn-Banach separation>, and <successive approximation for quotient operators> gives exact preimages.
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