Sentence examples for be a minimal subset from inspiring English sources

Using Zorn's Lemma, we obtain a minimal element K in F. Then K be a minimal subset of C with respect to being nonempty, closed, convex and satisfying the property.

Testor theory is a convenient way to solve this problem since a testor is defined as a subset of attributes that can discern between objects from different classes; and an irreducible testor is a minimal subset with this property.

Proof For each w ∈ M, let m ( w ) ⊂ S ( w ) be a minimal essential subset of S ( w ).

Proof For each q ∈ M, let m ( q ) ⊂ Λ ( q ) be a minimal essential subset of Λ ( q ).

Proof For each fixed q ∈ M 0, let m ( q ) ⊂ F ( q ) be a minimal essential subset of F ( q ).

Let W be a minimal nonempty hereditary subset of V. Then for any two vertices (w_1,W_2in W) the vertex (w_2) is a descendant of (w_1).

Let W be a minimal nonempty hereditary subset of V. Then the ideal I(W) is generated (as an ideal) by all idempotents (e_w, w in W).

Let B be a minimal path in G and (L subset B) be a lower bound of B. If L is not a start set, there exists (Uin V(L)) and (V in V(G)) such that (U neq V) and there is a path from V to U. Then (B setminus{U}) is a path in G and (B setminus{U} subset B).

Let ( X, M ) be a minimal space and A be a nonempty subset of X.

Let ( X, M ) be a minimal space and Y be a nonempty subset of X.

An essential subset m ( q ) ⊂ F ( q ) is said to be a minimal essential set of F ( q ) if it is a minimal element of the family of essential sets in F ( q ) ordered by set inclusion.