Sentence examples for a subnet of a from inspiring English sources

By (a) we have T ( A ) ¯ is compact and hence { b U } has a subnet converging to b 0. We may assume that b U ⟶ b 0. Since X is Hausdorff, there is a subnet of a U converging to b 0. The fact that b 0 ∈ T ( b 0 ) follows from ( a U, b U ) ∈ Graph ( T ) and the fact that Graph ( T ) is closed.

The edge-set E is assumed as a distinct unordered pairs of distinct elements of a set V. A subnet of the network having vertex set V and edge set E is a network having vertex-set V′ and edge-set E′ contained in V and E respectively.

If lim s f (s) = a for some a ∈ ℝ and {s'} is a subnet of {s} satisfying s' ≻ s for each s, then μ s ′ ( f ( s ′ ) ) = a.

Hence, there exists a subnet of such that.

Taking a subnet of such that exists, we obtain.

Consider a subnet of such that exists for every.

The above argument shows that, for every subnet of, there exists a subnet of such that { T μ α β x } Δ-converges to T μ x(= Px).

Since is compact valued, there exists a subnet of such that.

Let be a subnet of which is weak*-convergent to and such that exists.

Since is u.s.c. and compact-valued, it follows from Lemma 2.6 that there exist and a subnet of, we still denote this subnet by such that.

In addition, is u.s.c. and compact valued, it follows from Lemma 2.6 that there exist and a subnet of, we still denote this subnet by, such that.