Sentence examples for approximate selection from inspiring English sources

We establish new approximate selection theorems for almost lower semicontinuous multimaps with n-connectedness.

Our results unify and extend the approximate selection theorems in [1 3, 5 9].

We also establish some approximate selection theorems for almost lower semicontinuous multimaps in D-spaces and apply the results to topological semilattices with path connected intervals.

Our results unify and extend the approximate selection theorems in many published works and are applied to topological semilattices with path-connected intervals.

On the other hand, in LC-spaces, Wu and Li [6] obtained the approximate selection theorems for quasi-lower semicontinuous multimaps which were generalized by the author and Lee [7] to almost lower semicontinuous multimaps in C-spaces.

In this paper, we establish a new approximate selection theorem for almost lower semicontinuous multimaps with D-set values except on a set of topological dimension less than or equal to zero in LD-spaces.

With Proposition 3.1, we establish the V-approximate selection theorem which is the key result of this paper.

Then F is alsc if and only if F has a V-approximate selection for each V ∈ U.

For ϵ > 0, f is called an ϵ-approximate selection of F if for all x ∈ X, f ( x ) ∈ B ( F ( x ), ϵ ).

Then, for each V ∈ U, F has a V-approximate selection f : X → Y such that f ( x ) ∉ T ( x ). for all x ∈ X.

For V ∈ U, a continuous function f : X → Y is called a V-approximate selection of F if for all x ∈ X, f ( x ) ∈ V ( F ( x ) ).