Sentence examples for closure of a set from inspiring English sources

This means that (u_(cdot)in cl (U)), where cl denotes the closure of a set.

The boundary and the closure of a set S in ({mathbf{R}}^{n}) are denoted by ∂S and S̅, respectively.

We denote by and, the set of positive integers and the closure (weak closure) of a set in, respectively.

An achievable rate region is the closure of a set of achievable rate tuples for fixed {t m }.

The boundary and the closure of a set E in (mathbf{R}^{n}) are denoted by ∂E and E̅, respectively.

The sets ∂E and E̅ denote the boundary and the closure of a set E in ({R}^{n}).

In a minimal space ( X, M ), a set A ∈ P ( X ) is said to be an m-open set if A ∈ M. Similarly, a set B ∈ P ( X ) is an m-closed set if B c ∈ M. Furthermore, m-interior andm-closure of a set A are defined as follows: m - Int ( A ) = ⋃ { U : U ⊆ A, U ∈ M } and m - Cl ( A ) = ⋂ { F : A ⊆ F, F c ∈ M }.

Using a composition table, algebraic closure for a set of OPRAm statements is very useful for solving spatial navigation tasks.

Note that and the closure of a convex set is convex, then is a convex set.

It is shown in [3] that two conditions about the weak closure of a certain set consisting of normalized vectors and the asymptotic behavior of the operator C at infinity of λ, called normalized conditions, are main ingredients in solving an eigenvalue problem.

Let be an invariant set under. is said to be an admissible invariant set for if (a) is the closure of an open set in, that is, ; (b) if for some and in as for some, then in ; (c) if such that in, then in ; (d) for any, for.