Comment on (Soft Mappings Space)

One of the celebrated findings obtained in general topology reports that every compact subset of a Hausdorff space is closed. In this investigation, we demonstrate that this finding need not be true via soft topology. In 2014, Ozturk and Bayramov [1] discussed some properties of a soft Hausdorff space which defined in [2, 3] and its relationships with a soft compactness notion. However, they made an error, as we observe, in [Theorem 34, p.p.5] which investigated a relationship between soft closed set and soft compact Hausdorff space. To illustrate this mistake, we provide a counterexample and then we conclude under what conditions this result can be generalized via soft topology. We draw the attention of the readers to the fact that there are different kinds of soft Hausdorff spaces introduced in the literature. Some of them depend on the distinct ordinary points (see, for example, [2–4]) and the others depend on the distinct soft points (see, for example, [5–7]). First of all, we recall the following three definitions which will be needed throughout this manuscript. Definition 1 (see [2, 3]). — A soft topological space (X, τ, A) is said to be a soft T2-space (or soft Hausdorff) if for every x ≠ y ∈ X, there are two disjoint soft open sets (G, A) and (F, A) such that x ∈ (G, A) and y ∈ (F, A).