Sentence examples for closed points from inspiring English sources

If Prim(A) has a dense Gδ consisting of closed points (for instance, if Prim(A) is a T1-space) and A is unital, then Mloc(A) is its own local multiplier algebra and has only inner derivations.

Different methods have been developed to evaluate the accordance between measured and calculated doses, such as the point-to-point dose difference or the evaluation of the distance between two closed points having the same dose value.

since z + z 1 2 ∈ A ∩ B, since A ∩ B is convex, or all points in the segment [ z, z 1 ] ⊂ A ∩ B, again since A ∩ B is convex, are fixed points of the self-mappings S, S ∘ T : A ∪ B → A ∪ B. Now, take arbitrarily closed points z ′, z ″ = z ′ + ∈ ( z, z 1 ), which are also fixed points.

Both results implied that the Continuum Hypothesis is valid for all closed point sets.

In each of the spaces of Figures 1-9, a black jumbo dot means a pure open point, and further, the symbols ■ and mean a pure closed point and a mixed point, respectively.

The Cantor-Bendixson theorem then states that a closed point set can be decomposed into two subsets R and S, such that R is denumerable and S is perfect (indeed, S is the ath derived set of P, for a countable ordinal a).

At some point though, I started to realize that I was seeing things from a closed point of view.

Let be two Banach spaces, a proper closed convex and pointed cone with apex at the origin and, and that a family of closed, pointed, and convex cones in such that for all.

In this section we intend to obtain similar results as those from Theorem 3.2 when we know that the contractive conditions are satisfied only for closed enough points.

Let be a nonempty closed convex subset of, let be a closed convex pointed cone with, and let be a set-valued map.

Let be a nonempty closed convex subset of and let be a closed convex pointed cone with.