Sentence examples for m is compact from inspiring English sources
If cl ( T ( M ) ) is compact, f is continuous and linear and T is f-nonexpansive on M, then M ∩ F ( T ) ∩ F ( f ) ≠ ∅.
Let M be an oriented real differentiable manifold of real dimension 2n, for simplicity let's assume that M is compact.
Let M be a nonempty subset of a normed space X and let T and f be self-maps of M. Suppose that F ( f ) is q-starshaped, clT ( F ( f ) ) ⊆ F ( f ), cl ( T ( M ) ) is compact, T is continuous on M and (2.2) holds for all x, y ∈ M. Then M ∩ F ( T ) ∩ F ( f ) ≠ ∅.
If cl ( T ( M ) ) is compact, then, for each n ∈ N, cl ( T n ( M ) ) is compact and hence complete.
In this case, the operator C φ D m is compact on LB.
Let G be a unimodular Lie group acting freely and properly by holomorphic transformations on M so that M / G is compact.
Lemma 2.1 X ( I ; M ), X qcv ( I ; M ), and X qcc ( I ; M ) are compact convex subsets of C 0 ( I, R ).
Such level sets are therefore themselves compact ARs, and the values (argmin_{Psi (u)}varphi u,y,cdot)) of the map M are compact (R_{delta} -sets in view of Example 6(iii) above.
Let D be a closed convex subset of a Banach space X and 0 ∈ D. Assume that F : D → X is a continuous map which satisfies Monch's condition, that is, ( M ⊆ D is countable, M ⊆ co ¯ ( { 0 } ∪ F ( M ) ) ⇒ M ¯ is compact).
Let D be a closed convex subset of a Banach space X and 0 ∈ D. Assume that F : D → X is a continuous map which satisfies Mon̈ch's condition, that is, ( M ⊆ D is countable, M ⊆ c o ¯ ( { 0 } ∪ F ( M ) ) ⇒ M ¯ is compact).
