Sentence examples for be a soft compact from inspiring English sources
Then every soft compact set in F is soft closed in F. Proof Let K be a soft compact set in ( F, τ ˜ ) and let α ∈ ˜ K c ˜.
Proposition 5.2 Let ( K, τ ˜ ) be a soft compact topological space and let T : K → ˜ K be a soft continuous mapping.
Theorem 6.1 Let ( K, τ ˜ ) be a soft compact Hausdorff topological space and let T : K → ˜ K be a soft continuous mapping such that: 1. for each nonempty soft element α ∈ ˜ K, T is a nonempty soft element of K, 2.
Then the soft elements ( p 1, { u 2 } ), ( p 3, ∅ ) are the fixed points of T 2. Proposition 6.1 Let ( F, τ ˜ ) be a soft compact topological space and let { C n : n ∈ N } be a family of soft subsets of F satisfying: 1. C n ≠ ∅ ˜ for each n ∈ N, 2.
Thus, T ( K ) is a soft compact set.
Then T ( K ) is a soft compact set in ( K, τ ˜ ).
When we consider a soft topology τ ˜ as a family of all soft subsets of F, then clearly ( F, τ ˜ ) is not a soft compact topological space.
Definition 4.6 Let ( F, τ ˜ ) be a soft topological space and let K ⊆ ˜ F. We say that the soft set K is compact in ( F, τ ˜ ) if the soft topological space ( K, τ ˜ K ) is soft compact.
Next, we investigate soft topological spaces and formulate the definitions and deliver some properties of a soft compact topological space.
Zakharchenko was a soft touch.
