Sentence examples for exists a countable set of from inspiring English sources

Hence there exists a countable set of linearly independent functions ({varphi_{i}}_{i=1}^{infty}subseteq C_{0}^{infty }(Omega)) consists a basis of (V_{t}(Omega)).

Then there exists a countable set D0 ⊂ D, such that α(D) ≤ 2α(D0).

Then there exists a countable set (D_{0} subset D), such that (alpha(D) leq2alpha(D_{0})).

Then there exists a countable set (D_{0} subset D) such that (alpha (D) leq 2alpha (D_{0})).

Then there exists a countable set (B_{0} subset B), such that (alpha(B) leq2alpha(B_{0})).

Let be an ordered topological space, is said to be a quasi-separable set in if for any totally ordered set in, there exists a countable set such that is dense in (i.e., for any, there exists such that ).

If m h = 0, there exists a countable set { n i } such that lim n i → + ∞ x n i ( t n i ) = 0.

For any (Dsubset H), by Lemma 2.2, there exists a countable set (D_{0} = {u_{n}} subset D), such that alphabigl(Q(D bigr)leq2alphabigl(Q(D_{0} bigr).

For any (Wsubset B), by Lemma 2.3, there exists a countable set (W_{0} = {u_{n}} subset W), such that betabigl(Q(W bigr)leq2betabigl(Q(W_{0} bigr).

Then exist a countable set, such that.

Indeed, it will be proved there that there exists, at least, a countable set of countable families of critical points in which, only the first one can be obtained by the L-S min-max approach.