| 单词 | injection map |
| 释义 | > as lemmasinjection map(ping) 5. Mathematics. Also injection map(ping). A one-to-one transformation, esp. (formerly) an inclusion. ΘΚΠ the world > relative properties > number > arithmetic or algebraic operations > transformation > [noun] > correspondence > preserving relations or elements inclusion1870 orthomorphosis1885 isomorphism1892 identity1910 homoeomorphism1918 homomorphism1935 topological mapping or transformation1939 isometry1941 Möbius transformation1941 injection map(ping)1950 monomorphism1954 bijection1963 surjection1964 1950 S. MacLane in Bull. Amer. Math. Soc. LVI. 488 If S is a subgroup of G (notation S ⊂ G), then the injection κ..of S into G is that homomorphism of S into G with κ(s) = s for every s ∈ S. 1963 D. Bushaw Elem. Gen. Topol. 147 If X is a subset of Y, the function j:X → Y defined by j(x) = x is called the injection map from X to Y. The injection map from X to X is called the identity map on X. 1968 E. T. Copson Metric Spaces vii. 86 If the inverse image of each point of E2 is either empty or consists of a single point of E1, the mapping f:E1 → E2 is said to be an injection or a one-to-one mapping. If f:E1 → E2 is an injection, f(x1) = f(x2) implies x1 = x2; and x1 ≠ x2 implies f(x1) ≠ f(x2). < as lemmas |
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