In some special cases, however, the number of surjections A→B can be identified.

Let J=∩ᵢm_i be the (irredundant) primary decomposition of J. We associate to the pair (J,ω) the element ∑ᵢ(m_i,ωᵢ)∈G, where ωᵢ is the equivalence class of surjections from L/m_iL⊕(A/m_i)ⁿ⁻¹ to m_i/m_i² induced by ω.

In Banach space theory, a mapping u:E→F (between Banach spaces) is called a metric surjection if it is onto and if the associated mapping from E/ker(u) to F is an isometric isomorphism. Moreover, by the classical open mapping theorem, u is a surjection iff the associated mapping from E/ker(u) to F is an isomorphism.

Surjection

Meaning

Noun

Synonyms