surjective


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surjective

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An extremal ray R defines a proper surjective morphism with connected fibers [Cont.sub.R] : X [right arrow] Y such that, for an irreducible curve C [subset] X, [Cont.sub.R](C) is a point if and only if [C] [member of] R.
where [W.sup.K] is the matrix whose columns are the coefficients of the functions of the basis [[psi].sup.K] written in the basis [[empty set].sup.k-1] and [[PHI].sup.k] is the matrix that represents a surjective transformation from [V.sup.k] in [??].
If two semirings S and T have weak local units and there exists a unitary Morita context (S,T,[.sub.S][P.sub.T,T][Q.sub.S],[theta],[phi]) with [theta],[phi] surjective, then there is a quantale isomorphism Id(S) [right arrow] Id(T) that takes finitely generated ideals to finitely generated ideals.
Since [g.sub.2] is surjective, there exists [x.sub.1] [member of] X such that [g.sub.2]([x.sub.1]) [member of] [T.sub.1][x.sub.0] and ([g.sub.1]([x.sub.0]), [g.sub.2]([x.sub.1])) [member of] E(G).
Now the Tietze-Urysohn Theorem shows that to prove the corollary it is sufficient to construct a linear continuous surjective map T from [C.sub.p](I) onto [C.sub.p]([I.sup.n]).
Since f is a surjective quantale homomorphism and [[bar.H].sub.1] (A) is an ideal of [Q.sub.t], we have xvz = f([x.sub.1]) [disjunction] f([z.sub.1]) = f([x.sub.1] [disjunction] [z.sub.1]) [member of]f([H.sub.1] (A)).
(ii) Since [phi] is surjective, [[phi].sup.[left arrow].sub.L]([mu]) = [0.bar] implies [mu] = [0.bar].
In this section, we shall determine the structure of surjective maps on density operators preserving Tsallis entropy of convex combinations.
Silvestrov, "Unital algebras of Hom-associative type and surjective or injective twistings," Journal of Generalized Lie Theory and Applications, vol.
(iii) T + C is surjective if T is expansive and C is compact;
i) There is no map f : W [right arrow] M which is a strongly surjective map if W is a CW-complex with [H.sup.3](W;Z) = 0 and M is either [S.sup.1] x [S.sup.2], [S.sup.1] x [S.sup.1] x [S.sup.1], or a lens space;
Among specific topics are sparse hamburger moment multi-sequences, surjective isometries on absolutely continuous vector valued function spaces, extensions of isometries in generalized gyrovector spaces of the positive cones, kernels of adjoints of composition operators with rational symbols of degree two, and associating linear and nonlinear operators.