Almost compactness in fuzzy topological spaces

We introduce and study almost compactness for fuzzy topological spaces. We show that the almost continuous image of an almost compact fuzzy topological space is almost compact. Moreover, we show that generally almost compactness for fuzzy topological spaces is not product-invariant, but if X and Y are almost fuzzy topological spaces and X is product related to Y, then their fuzzy topological product is almost compact.     

A comparison of different compactness notions in fuzzy topological spaces

Starting from a defining differential equation $\text{(}\text{?}\text{?t}\text{) W(λ, t, u) = (}\text{λ(u ? t)}\text{p(t)}\text{) W(λ, t, u)}$ of the kernel of an exponential operator $\text{S}{}_{\mathrm{\lambda }}\text{(?, t) = ∫}{}_{\mathrm{?\infty }}{}^{\mathrm{\infty }}\text{W(λ, t, u)?(u) du}$ with normalization ∫_?∞^∞W(λ, t, u) du = 1, we determine S_λ for various p(t) including; for example, p(t) a quadratic polynomial, all the known exponential operators are recovered and some new ones are constructed. It is shown that all the exponential operators are approximation operators. Further approximation properties of these operators are discussed. For example, functions satisfying $\text{∥ S}{}_{\mathrm{\lambda }}\text{(?, t) ? ?(t)∥ = O(λ}{}^{\mathrm{?\alpha }}\text{)}$ are characterized. Several results of C. P. May are also improved.     

Fuzzy points and local properties of fuzzy topological spaces

We prove that three theorems of C.K. Wong on local properties of fuzzy topology are wrong, thereby we discuss his notions of fuzzy point, C₁, separability, and local compactness.     

On fuzzy topological spaces

In this note the concept of almost fuzzy continuous mapping from a fuzzy topological space into another is introduced and discussed.     

C-scattered fuzzy topological spaces

In this paper, we define the concept of C-scattered fuzzy topological spaces and obtain some properties about them. In particular, we study the relation between C-scattered spaces and its fuzzy extension, it is proved that C-scattered fuzzy topological spaces are invariant by fuzzy perfect maps, and that, in the realm of paracompact fuzzy topological spaces, the C-scattered spaces verify that their product by other fuzzy spaces is also paracompact fuzzy.     

On fuzzy topological spaces

In this paper, a few separation properties and some aspects of subspace fuzzy topology have been studied, where both the crisp and the fuzzy elements have been taken into consideration. Since the conventional definition of compactness is not quite meaningful in Hausdorff fuzzy spaces (as introduced by us), a new more natural definition of proper compactness is given and a few properties resulting from this are established.     

Compact Hausdorff fuzzy topological spaces are topological

Many examples of compact fuzzy topological spaces which are highly non topological are known [5, 6]. Equally many examples of Hausdorff fuzzy topological spaces which are highly non topological can be given. In this paper we show that the two properties - compact and Hausdorff - combined however necessarily imply that the fuzzy topological space is topological. This at once solves some open questions with regard to the compactification of fuzzy topological spaces [8]. It also emphasizes once more the particular role played by compact Hausdorff topological spaces not only in the category of topological spaces but even in the category of fuzzy topological spaces.     

Fuzzy Hausdorff topological spaces

We introduce the notion of a fuzzy Hausdorff topological space and make a few observations to establish the appropriateness of this notion.     

Intuitionistic supra fuzzy topological spaces

In this paper, We introduce an intuitionistic supra fuzzy closure space and investigate the relationship between intuitionistic supra fuzzy topological spaces and intuitionistic supra fuzzy closure spaces. Moreover, we can obtain intuitionistic supra fuzzy topological space induced by an intuitionistic fuzzy bitopological space. We study the relationship between intuitionistic supra fuzzy closure space and the intuitionistic supra fuzzy topological space induced by an intuitionistic fuzzy bitopological space.     

R1 fuzzy topological spaces

A fuzzy topological analog of the R₁ separation axiom of topology is introduced and its appropriateness is established.     

Compactness in fuzzy topological spaces

Since earlier approaches to compactness in fuzzy spaces have serious limitations, we propose a new definition of fuzzy space compactness. In doing so, we observe that it is possible to have degrees of compactness, which we call α-compactness (α a member of a designated lattice). We obtain a Tychonoff Theorem for an arbitrary product of α-compact fuzzy spaces and a 1-point compactification. We prove that the fuzzy unit interval is α-compact.     

α-compact fuzzy topological spaces

The purpose of this paper is to introduce and discuss the concept of α-compactness for fuzzy topological spaces. And we obtain a product theorem for an arbitrary product of α-compact fuzzy spaces.     

Suitability in fuzzy topological spaces

An L-fuzzy topological space is said to be suitable if it possesses a nontrivial crisp closed subset. Basic properties of and sufficient conditions for suitable spaces are derived. Characterizations of the suitable subspaces of the fuzzy unit interval, the fuzzy open unit interval, and the fuzzy real line are obtained. Suitability is L-fuzzy productive; nondegenerate 1¹-Hausdorff spaces are suitable; the fuzzy unit interval, the fuzzy open unit interval, and the fuzzy real line are not suitable; and no suitable subspace of the fuzzy unit interval, the fuzzy open unit interval, or the fuzzy real line is a fuzzy retract of the fuzzy unit interval, the fuzzy open unit interval, or the fuzzy real line, respectively. Without restrictions there cannot be a fuzzy extension theorem.