A {\displaystyle A} is a subset of B , {\displaystyle B,} then the inclusion map is the function ι {\displaystyle \iota } that sends each element x {\displaystyle...

Boolean analogue to the subset relation Inclusion map, or inclusion function, or canonical injection Inclusion (logic), the concept that all the contents...

S} which itself has the structure of a manifold, and for which the inclusion map S → M {\displaystyle S\rightarrow M} satisfies certain properties. There...

exotic inclusion map S5 → S6 as a transitive subgroup (the obvious inclusion map Sn → Sn+1 fixes a point and thus is not transitive) and, while this map does...

In combinatorics, the inclusion–exclusion principle is a counting technique which generalizes the familiar method of obtaining the number of elements...

f:A\hookrightarrow B} ), although some authors specifically reserve ↪ for an inclusion map. For visual examples, readers are directed to the gallery section. For...

subspace of Y and g : Z → Y is the inclusion map we can "glue" Y to another space X along Z using an "attaching map" f : Z → X. The result is the adjunction...

Y → X {\displaystyle i:Y\to X} be the inclusion map. Then for any topological space Z {\displaystyle Z} a map f : Z → Y {\displaystyle f:Z\to Y} is continuous...

always continuous. The identity function is idempotent. Identity matrix Inclusion map Indicator function Knapp, Anthony W. (2006), Basic algebra, Springer...

normal subgroup of G. In particular, if H is a subgroup of G, then the inclusion map i from H to G is a monomorphism, and will be normal if and only if H...

→ Y is a continuous pointed map, then the preimage of the distinguished point, K, is a subspace of X. The inclusion map of K into X is the categorical...

X {\displaystyle X} is essential for the inclusion map to be a local homeomorphism because the inclusion map of a non-open subset of X {\displaystyle...

of monoids, Mon, the inclusion map N → Z is a non-surjective epimorphism. To see this, suppose that g1 and g2 are two distinct maps from Z to some monoid...

interpreted by means of the fiber product of schemes, applied to f and the inclusion map of Y ′ {\displaystyle Y'} into Y. For the second, the idea is that morphisms...

\iota :\mathbf {H} _{R}^{1(n)}\rightarrow \mathbf {M} ^{n+1}} is the inclusion map and the superscript star denotes the pullback. The present purpose is...

are as above, we say that U {\displaystyle U} can be excised if the inclusion map of the pair ( X ∖ U , A ∖ U ) {\displaystyle (X\setminus U,A\setminus...

is said to be well-pointed if the inclusion map x → X {\displaystyle {x}\to X} is a cofibration. The inclusion map S n − 1 → D n {\displaystyle S^{n-1}\to...

{\displaystyle T_{W}} is also self-adjoint. When V is replaced by the inclusion map I : W → H {\displaystyle I:W\to H} , V ∗ = I ∗ = P K : H → W {\displaystyle...

is an isometry if X {\displaystyle X} is a Banach space. Denote the inclusion map by In : M → X  where  In ⁡ ( m ) := m  for all  m ∈ M . {\displaystyle...

well as in Southern Africa, to map the distribution of different diamond source regions. Sub-lithospheric mineral inclusions such as majorite and silicate...

function, namely the quotient map. The disjoint union topology is the final topology with respect to the inclusion maps. The final topology is also the...

following commutative diagram: Here i is the inclusion map and ΦX, ΦY are the maps obtained by composing the quotient map with the canonical injections into the...

is also Hamiltonian, with momentum map the composition of the inclusion map with M {\displaystyle M} 's momentum map. Suppose that the action of a Lie...

the inclusion map Spec ⁡ ( R / I ) → Spec ⁡ ( R ) {\displaystyle \operatorname {Spec} (R/I)\to \operatorname {Spec} (R)} induced by the canonical map R...

denote the inclusion map by In K L : C k ( K ) → C k ( L ) . {\displaystyle \operatorname {In} _{K}^{L}:C^{k}(K)\to C^{k}(L).} Then this map is a linear...

general convention, and the latter notation is more commonly used for inclusion maps or embeddings.[citation needed] Specifically, for a partial function...

three-dimensional submanifold, called the compact core or Scott core, such that its inclusion map induces an isomorphism on fundamental groups. In particular, this means...

\{U_{i}\}_{1\leq i\leq k}} of X {\displaystyle X} with the property that each inclusion map U i ↪ X {\displaystyle U_{i}\hookrightarrow X} is nullhomotopic. For...

Riemannian submanifold of R n + 1 {\displaystyle \mathbb {R} ^{n+1}} via the inclusion map S n ↪ R n + 1 {\displaystyle S^{n}\hookrightarrow \mathbb {R} ^{n+1}}...

subspace with respect to the inclusion map. The product topology is the initial topology with respect to the family of projection maps. The inverse limit of...