The phrase "a soft group" is correct and usable in written English.
It can be used to describe a group of people or entities that are gentle, non-confrontational, or easygoing in nature.
Example: "The team was known for being a soft group, always prioritizing collaboration and understanding over competition."
Alternatives: "a gentle group" or "a mild group".
Therefore, (F,A) is a soft group over X.
Let (F,A) be a soft group over G1 and f : G1 → G2 be a homomorphism.
It is clear that (f−1 (G),A) is a soft group over X and f−1 is a soft topology on X.
It is clear that (f(F ,A) is a soft group over Y and f is a soft topology on Y.
Let {(F i,A); i ∈ I} be a nonempty family of soft groups of G where I is an index set, and then ⋂ ~ i ∈ I ( F i, A ) Open image in new window is a soft group over G[6].
Let (F,A) be a soft group over G, and then[6] (i) (F,A) is said to be an identity soft group over G if F x) = {e}, for all x ∈ A, where e is the identity element of G. (ii) (F,A) is said to be an absolute soft group if F x) = G, for all x ∈ A. .
Let F : A → G Open image in new window be a mapping, and then (F A) will be called a generalized soft group.
Define a mapping F N Open image in new window over A by F N = Open image in new window the factor group F N , for all α ∈ A. Open image in new window Therefore, ( F N, A ) Open image in new window is a factor soft group.
If ϕ α : ( F 1 , τ F 1 → ( F 2 , ν F 2 Open image in new window be the corresponding homomorphism for each α ∈ A, then. (i) (ϕ F1,A,ν) is a soft topological soft group over Y and ( ϕ F 1, A, ν ) ≤ ~ ( F 2, A, ν ) Open image in new window.
If (N,A) be a soft subgroup of (F,A), then (N,A,τ) is a soft topological soft group over X and (N,A,τ) is a soft topological soft subgroup of (F,A,τ).
By Theorem 22, (ϕ F 1,A,ν) is a soft topological soft group over Y and ( ϕ F 1, A, ν ) ≤ ~ ( F 2, A, ν ) Open image in new window.
