Sentence examples for locally complete from inspiring English sources
However, we give the following examples of spaces which are not locally complete but the condition on local completeness of some related subsets is satisfied.
Assuming that is a locally complete locally convex space, the condition on local completeness of some related subsets is automatically satisfied.
We follow the local close world assumption (LCWA) [20], assuming that G is locally complete, i.e., either G includes the complete neighbors of a node for any edge type, or it has no information about these neighbors.
Hence, if is locally complete, then is locally complete.
If the set is locally complete, then is locally complete and if is locally complete, then is locally complete.
If or is locally complete, then is locally complete, so is locally complete.
These blocks are then locally completed by adding neighboring syntenic homologs that are not reciprocal best hits (>30% similarity over 50% of the smallest protein).
The following theorem states the existence of the random fixed points for lower semicontinuous correspondences defined on locally compact complete metric spaces.
Theorem 4.1 Let ( Ω, F ) be a measurable space, C be a closed separable subset of a locally compact complete metric space and let T : Ω × C → 2 X be a lower semicontinuous random operator with closed values.
The existence of the random fixed points remains valid if for each ω ∈ Ω, ( T − 1 : X → 2 C is lower semicontinuous. In this case, we establish Theorem 4.2. Theorem 4.2 Let ( Ω, F ) be a measurable space, C be a closed separable subset of a locally compact complete metric space and let T : Ω × C → 2 X be an operator with closed values.
Corollary 4.2 Let ( Ω, F ) be a measurable space, C be a closed separable subset of a locally compact complete metric space and let T : Ω × C → 2 X be a random operator which enjoys condition α and has closed values, such that for each ω ∈ Ω, ( T − 1 : C → 2 C is closed valued. Suppose that, for each ω ∈ Ω, the set F : = { x ∈ C : x ∈ T ( ω, x ) } ≠ ∅.
