In one variant, the key is a geometric fact that there exists a partition of unity ({J_{mathcal {C}}}_{{mathcal {C}}ne {mathcal {C}}_{min}}) indexed non-minimal partitions so that (sum _{{mathcal {C}}} J_{mathcal {C}}= {varvec{1}}) and so that on ({text {supp}}J_{mathcal {C}}cap {x,|, |x| > 1}), one has that, for some (Q>0), (|x_j-x_k| ge Q|x|) if ((jk) not subset {mathcal {C}}).
By a partition of unity, there exists a family { β i } i = 1 n of real-valued continuous functions subordinate to { M y i } i = 1 n such that for all x ∈ K, 0 ≤ β i ( x ) ≤ 1 and ∑ i = 1 n β i ( x ) = 1 and for each x ∉ M y i, β i ( x ) = 0. Let C : = co { y 1, y 2, …, y n } ⊆ K. Then C is a simplex of a finite dimensional space.
For us, however, it is sufficient to observe that all unities are propositions or propositional concepts, and that consequently nothing that exists is a unity.
Since X is para-compact, there exists a continuous partition of unity {β0, β p : p ∈ LF(E)} for X subordinated to the open cover {V0, V p : p ∈ LF(E)}.
Since is paracompact, there exists a continuous partition of unity for subordinated to the covering (see Dugundji [22, Theorem VIII, 4.2]); that is, for any, and are continuous functions such that, for any, for all and for all and, is locally finite and for any.
He has also proposed something that has never actually existed in America: a unity government to pull the country back from the brink.
I realized our power exists in unity.
In a blog post, the company calls the engine "a layer that exists between the Unity game engine and real-world hand physics".
The force is not elsewhere, it exists in our unity.
