Linked from

The 15 pages that link to Surjective function, each with the reason it gives.

• FunctionBroader topic: Surjectivity requires every allowed codomain element to be attained.

• Inverse functionRelated: Surjectivity ensures every element of the codomain has an inverse image.

• Pigeonhole principleRelated: When every container is occupied, excess objects still force some container to receive multiple inputs.

• BijectionRelated: This property ensures the function reaches the entire codomain.

• IsometryRelated: Distance preservation alone does not guarantee that every target point is reached.

• Injective functionCompared with: Surjectivity requires reaching every declared output, unlike injectivity's restriction on repeated outputs.

• CodomainRelated: Surjectivity tests whether every element of the specified target is reached.

• Image (mathematics)Related: Surjectivity is precisely the condition that every declared output is attained.

• Stirling numbers of the second kindRelated: Labeling k blocks turns each partition into k! surjections onto a fixed k-element set.

• Open mapping theoremRelated: Surjectivity ensures the target is covered by images of scaled balls in the domain.

• Partition of a setRelated: The nonempty fibers of a surjection partition its domain.

• Left inverseCompared with: Surjectivity is not needed for a left inverse, but it is needed for a right inverse.

• Range of a functionRelated: Surjectivity is the condition that every codomain value is attained.

• Mazur–Ulam theoremRelated: Surjectivity allows the proof to compare reflected images across the entire target space.

• Twelvefold wayRelated: Requiring every distinguishable box to be occupied is exactly surjectivity.