Sentence examples for be any nonempty subset from inspiring English sources

Let (( X,p ) ) be a partial metric space and A be any nonempty subset of X.

Let A be any nonempty subset of a metric space ( X, d ).

Remark 9 Let ( X, d ) be a metric space and A be any nonempty subset of X.

Let (( X,p ) ) be a partial metric space and A be any nonempty subset of X, then (ainoverline{A}) if and only if (p ( a,A ) =p ( a,a ) ). [18].

Let V ( x ) : = inf y ∈ S ( x ) ξ ( D, C ) ( F ( x, y ) ), where ξ ( D, C ) ( z ) : = inf { r ∈ R : z ∈ r D − C } for all z ∈ Y. Let W be any nonempty subset of A which is well ordered by a relation s satisfying u s v ⇒ u r ∗ v for every  u, v ∈ W, u ≠ v.

Let U and V be any nonempty subsets in X.

Let (widetilde{U}) be any nonempty open subset in (lim_{leftarrow} X,f)).

Let (widetilde{U}_{i}) ((i=1,2,ldots,p)) be any nonempty open subset in (lim_{leftarrow} X,f)).

Let E be a Banach space and Ω be any nonempty closed subset of E. If M is a contraction of Ω into itself, then the mapping M has a unique fixed point, i.e., there exists a unique x ∈ Ω such that x = M x.

Let (widetilde{U}) and (widetilde{V}) be any nonempty open subsets (lim_{leftarrow} X,f)).

Let be any nonempty closed convex subset of a Banach space and a quasi-contraction mapping.