Sentence examples for be a compact Lie from inspiring English sources

Let G be a compact Lie group.

Let G be a compact Lie group, and let g be its Lie algebra.

Let G be a compact Lie group, L G) the associated loop group, ω the canonical symplectic form on L(G).

Let ((X, xi )) be a compact Kähler manifold.

Let X be a compact ANR-space and (rcolon Xto B) be a retraction map.

Let X be a compact ANR-space and (varphiin A X,X)).

Let ((Sigma,g)) be a compact Riemannian surface without boundary, h be in (C^{0}(Sigma )) with (hgeq0) and (hnotequiv0).

Let (Bsubset X) also be a compact ANR-space and (varphiin A_{U}(X)) be such that (varphi(X subset B).

We note that if X is a compact Hausdorff space, then C ( X ) is a Banach space under pointwise algebraic operations and under the norm ∥ f ∥ = sup x ∈ X | f ( x ) |. Let X be a compact Hausdorff space and E be a subspace of C ( X ).

The following theorem goes often after the name of Lefschetz decomposition, and is essential in order to prove the third Lefschetz theorem (see 3). (i) Let ((X, xi )) be a compact Kähler manifold.

(Gromov's few relations theorem) Let X be a compact Kähler manifold and assume that there exists a surjection of its fundamental group begin{aligned} Gamma : = pi _1 (X) rightarrow G = langle x_1, ldots, x_n | R_1 x), ldots, R_m (x) rangle, end{aligned}onto a finitely presented group that has 'few relations', more precisely where ( n ge m-2).