Sentence examples for connected set such that from inspiring English sources
To this aim, let (Asubseteq Y) be a nonempty open connected set, such that (Q^(A)neemptyset ).
Thus, R can be set such that the moving sensors stay connected.
If there exists a nonempty compact convex subset of, and, such that, for all, then is a nonempty connected set.
It is said that F is arcwise connected D-quasiconvex if the generalized level set operatorname{Lev}_{F} y)=bigl{ xin S: mbox{there is }zin F x) mbox{ such that }y-zin D bigr} is an arcwise connected set for every point (yin Y).
Define a 2-cyclic self-mapping T A ∪ B → A ∪B with T(A)⊆ B and T(B)⊆ A for some sets A ⊂ R0+ := {z ∈ R z ≥ 0} and B ⊂ R0- := {z ∈ R z ≤ 0} being non-empty bounded connected sets containing {0}, so that D = 0, such that Tx k = x k +1; ∀k ∈ z0+ for the control sequence u k k ∈ Z 0 + lying in some appropriate class to be specified later on.
Assume that and are closed disjoint nonempty bounded simply connected sets with and for some,.
In the mathematical field of graph theory, a bipartite graph is a graph whose vertices can be divided into two disjoint sets ( mathbb{U} ) and ( mathbb{V} ) (that is, ( mathbb{U} ) and ( mathbb{V} ) are each independent sets) such that every edge connects a vertex in ( mathbb{U} ) to one in ( mathbb{V} ).
A space M is locally arcwise connected at a point x ∈ M if for any neighborhood U of x, there exists an arcwise connected open set V such that x ∈ V ⊂ U, and M is locally arcwise connected if it is locally arcwise connected at each point in M. Recall that each component of an open set in a locally arcwise connected space is open.
Polygon, In geometry, any closed curve consisting of a set of line segments (sides) connected such that no two segments cross.
We get a continuous path connecting and such that (5.19).
