Sentence examples for is closed under from inspiring English sources

An informal argument for Zorn's lemma can be given as follows: Assume that S is closed under unions of chains.

Taking S to be the collection of all linearly independent sets of vectors in V, it can be shown that S is closed under unions of chains.

The class is closed under convex combinations.

(A1) states that hard information is closed under (known) implications.

Proof We first show that Φ is closed under compositions.

Furthermore, we have Φ g is closed under compositions.

Since Φ ′ is closed under compositions, then f ¯ ∈ Φ ′.

which is closed under the operation of complex multiplication.

The class is closed under the following operations.

We also assume that K is closed under expansions and revisions.

Call a family of sets strongly reductive if it is closed under intersections of nests.