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Injective and surjective functions

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Injectiveness and Surjectiveness describe the mapping structure of functions as demonstrated by the following picture.

%3 cluster0 injective and surjective (bijective) cluster1 injective and non-surjective cluster3 injective and non-surjective cluster4 non-injective and non-surjective n0i1 i1 n0i2 i2 n0o1 o1 n0o2 o2 n0i1->n0o2 n0i3 i3 n0i2->n0o1 n0i4 i4 n0o3 o3 n0i3->n0o3 n0i5 i5 n0o4 o4 n0o5 o5 n0i4->n0o5 n0i5->n0o4 n3i1 i1 n3o1 o1 n1i1 i1 n1i2 i2 n1o1 o1 n1i1->n1o1 n1i3 i3 n1o2 o2 n1o3 o3 n1i2->n1o3 n1i4 i4 n1i3->n1o2 n1i5 i5 n1o4 o4 n1o5 o5 n1i4->n1o5 n1o6 o6 n1i5->n1o6 n4i1 i1 n4o1 o1 n3i2 i2 n3i1->n3o1 n3i3 i3 n3i2->n3o1 n3o2 o2 n3i4 i4 n3i3->n3o2 n3i5 i5 n3o4 o3 n3i4->n3o4 n3i5->n3o4 n4i2 i2 n4i1->n4o1 n4i3 i3 n4i2->n4o1 n4o2 o2 n4i4 i4 n4i3->n4o2 n4o3 o3 n4i5 i5 n4o4 o4 n4i4->n4o4 n4i5->n4o4 n4o5 o5 n4o6 o6

Tags: Functional Analysis

Categories: Mathematics


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