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: Let be a compact, closed surface ( not necessarily connected ).
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Let and be
Let the open enemy to it be regarded as a Pandora with her box opened ; ;
Let every policeman and park guard keep his eye on John and Jane Doe, lest one piece of bread be placed undetected and one bird survive.
`` Let him be now ''!!
Let us assume that it would be possible for an enemy to create an aerosol of the causative agent of epidemic typhus ( Rickettsia prowazwki ) over City A and that a large number of cases of typhus fever resulted therefrom.
Let T be a linear operator on the finite-dimensional vector space V over the field F.
Let p be the minimal polynomial for T, Af, where the Af, are distinct irreducible monic polynomials over F and the Af are positive integers.
Let Af be the null space of Af.
Let N be a linear operator on the vector space V.
Let T be a linear operator on the finite-dimensional vector space V over the field F.
Let V be a finite-dimensional vector space over an algebraically closed field F, e.g., the field of complex numbers.
Let N be a positive integer and let V be the space of all N times continuously differentiable functions F on the real line which satisfy the differential equation Af where Af are some fixed constants.
Let Q be a nonsingular quadric surface bearing reguli Af and Af, and let **zg be a Af curve of order K on Q.
Let us take a set of circumstances in which I happen to be interested on the legislative side and in which I think every one of us might naturally make such a statement.
Let the state of the stream leaving stage R be denoted by a vector Af and the operating variables of stage R by Af.
Let this be denoted by Af.
Let it be granted then that the theological differences in this area between Protestants and Roman Catholics appear to be irreconcilable.
Let not your heart be troubled, neither let it be afraid ''.
The same God who called this world into being when He said: `` Let there be light ''!!
For those who put their trust in Him He still says every day again: `` Let there be light ''!!
Let us therefore put first things first, and make sure of preserving the human race at whatever the temporary price may be ''.
Let her out, let her out -- that would be the solution, wouldn't it??
Let and compact
Let X be a locally compact Hausdorff space.
Let X be a locally compact Hausdorff space.
Let be the space of real-valued continuous functions on X which vanish at infinity ; that is, a continuous function f is in if, for every, there exists a compact set such that on
Let X be a normed topological vector space over F, compatible with the absolute value in F. Then in X *, the topological dual space X of continuous F-valued linear functionals on X, all norm-closed balls are compact in the weak -* topology.
Let K be a closed subset of a compact set T in R < sup > n </ sup > and let C < sub > K </ sub > be an open cover of K. Then
Let X be a locally compact Hausdorff space equipped with a finite Radon measure μ, and let Y be a σ-compact Hausdorff space with a σ-finite Radon measure ρ.
Let X be a compact complex manifold of complex dimension n. Then X is an orientable smooth manifold of real dimension 2n, so its cohomology groups lie in degrees zero through 2n.
* Let ρ be a unitary representation of a compact group G on a complex Hilbert space H. Then H splits into an orthogonal direct sum of irreducible finite-dimensional unitary representations of G.
Let G be a compact topological group, which we assume Hausdorff.
Let G be a compact, connected Lie group and let be the Lie algebra of G.
Let X be a compact Hausdorff space that satisfies the property that no one-point set is open.
Let X be a compact Hausdorff space.
Let M be a compact orientable 2n-dimensional Riemannian manifold without boundary, and let be the curvature form of the Levi-Civita connection.
Let be the set of smooth functions with compact support on the real line Then, the map
Let us extend to compact Lie group and consider " integrable " orbits for which the symplectic structure comes from a line bundle then quantization leads to the irreducible representations of.
Let be a compact oriented manifold of dimension.
A proof can be sketched as follows: Let Ω be the weak *- compact set of positive linear functionals on A with norm ≤ 1, and C ( Ω ) be the continuous functions on Ω.
Let denote the smallest integer so that all compact connected-manifolds embed in.
Let be vector bundles, equipped with metrics, on a compact manifold M with a volume form dV.
* K ( X, Y ) is a closed subspace of B ( X, Y ): Let T < sub > n </ sub >, n ∈ N, be a sequence of compact operators from one Banach space to the other, and suppose that T < sub > n </ sub > converges to T with respect to the operator norm.
Let be a continuous and compact mapping of a Banach space into itself, such that the set
Let V be a finite dimensional complex vector space, let H ⊂ Aut ( V ) be an irreducible semisimple complex connected Lie subgroup and let K ⊂ H be a maximal compact subgroup.
Let be a locally compact Hausdorff group.
Let be the compact cylinder where is defined, this is
Let have compact support and.
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