Exact(5)
For λ = 0, the assertion is obvious.
The second assertion is obvious by Lemma 3.4.
Proof For a = 0, the assertion is obvious.
The first assertion is obvious from the continual evolution of plans for the Dymaxion.
Altogether, we see that μ ( Ker ( f t ) ) = t, thus μ ( Ker ( f ) ) = n = | f | C. The last assertion is obvious: if 0 ⟶ K ′ ⟶ X ⟶ f Y ⟶ 0 is the universal extension from below with K ′ ∈ add K, then [ f 〉 belongs to C [ → Y 〉 and any other extension of Y from below with kernel in add K is induced from it. Thus [ f 〉 has to be the zero element of the lattice C [ → Y 〉. □.
Similar(55)
We will first show that there exists a positive number t 0 such that the equation H 1 ( t, s, x ) = 0 (2.2). has no solution x in D ( C ) ∩ ∂ Ω for all t ∈ ( 0, t 0 ] and all s ∈ [ 0, 1 ]. For s = 0, assertion (2.2) is obvious because ( T t + ε J ) x = 0 implies x = 0. Assume that assertion (2.2) does not hold for any s ∈ ( 0, 1 ].
Assertion (ii) is obvious [6].
Assertion (11) is obvious for m = 1.
Let us note that the assertion, opposite in a sense with to that statement of Theorem 2.2, is obvious.
It is obvious that this assertion remains true for an arbitrary function.
Hence, it is obvious that every -function is a -function and every -function is a -function, but the converse assertions do not hold.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com