Theorem 2.5 If (a6) holds and Ω is compact, then the following assertions are equivalent: (i) (GVQEP) is GTWP 2; (ii) Ω ≠ ∅ and there exists a forcing function with parameter c : S × T → R + (where S is the parameter set) such that (2.20) holds, where S and T are defined by (2.21). .
If, in addition, T is compact, then the following further assertions hold: ( c 4 ) the function δ is C 1, increasing and strictly concave in ] 0, θ [ ; ( c 5 ) one has L ( ω ˆ r ) − 2 δ ′ ( r ) ω ˆ r = z. for all r ∈ ] 0, θ [ ; ( c 6 ) one has δ ′ ( r ) = 1 2 k − 1 ( r ). for all r ∈ ] 0, θ [. Before giving the proof of Theorem 3.4, we establish the following.
Poincaré later extended his conjecture to any dimension, or, more specifically, to the assertion that every compact n-dimensional manifold is homotopy-equivalent to the n-sphere (each can be continuously deformed into the other) if and only if it is homeomorphic to the n-sphere.
Let A be a compact-supported subset of R F c. Then the following assertions are equivalent: A is a relatively compact subset of ( R F c, D ), A is level-equicontinuous on [ 0, 1 ].
Using that is strongly continuous and the property (H5), we infer that is relatively compact set, and, which establishes our assertion.
end{aligned} (3.10) The assertion (3.9) is just a compact form of (3.10).
Now, our assertion follows immediately by taking the compact K to be the image of the limit function γ : [ a, b ] → X. □.
There's a small compact of faith implicit in the attempt — an unfashionable assertion that one can use writing to stay alive.
This starts from the assertion that France has made a huge sacrifice of sovereignty by accepting the budgetary austerity inherent in the fiscal compact.
