Many scientists have studied and improved the soft set theory, which is initiated by Molodtsov [33] and easily applied to many problems having uncertainties from social life. The main purpose of our paper, is to introduce new soft separation axioms based on the b-open soft sets which are more general than of the open soft sets. We show that, the properties of soft b-Ti-spaces (i = 1,2) are soft...

in this paper, countable compactness and the lindel¨of propertyare defined for l-fuzzy sets, where l is a complete de morgan algebra. theydon’t rely on the structure of the basis lattice l and no distributivity is requiredin l. a fuzzy compact l-set is countably compact and has the lindel¨ofproperty. an l-set having the lindel¨of property is countably compact if andonly if it is fuzzy compact. ...

From now on we will work with sets A ⊂ X within a fixed rectangle X ⊂ R. Elementary sets in X make an algebra. Definition 1.8. The outer measure of a setA ⊂ X is μ∗(A) = inf ∑∞ i=1Area(Ri) where the infimum is taken over all countable covers of A by rectangles, A ⊂ ∪i=1Ri. Definition 1.9. The inner measure of a set A ⊂ X is μ∗(A) = Area(X)− μ∗(Ac) where A = X \ A is the complement of A. Lemma. ...

Molodstov introduced soft sets to deal with uncertainties and not clear objects. Researchers developed the relationship between soft sets and information systems. Fuzzification of the notions of soft sets and soft topology have been discussed in the literature. In this paper, we define and establish the topological structures of fuzzy soft semi-open sets and fuzzy soft semi-closed sets. We intr...

‎In this paper we have introduced new types of sets termed as $omega_{_{gamma_{_mu}}}$-open sets with the help of an operation and a generalized topology‎. ‎We have also defined a notion of $gamma_{_mu}$-Lindel"{o}f spaces and discussed some of its basic properties‎.  

We discuss fuzzy simplicial sets, and their relationship to something like metric spaces. Namely, we present an adjunction between the categories: a metric realization functor and fuzzy singular complex functor. The following document is a rough draft and may have (substantial) errors. 1. Fuzzy simplicial sets Let I denote the Grothendieck site whose objects are initial open intervals contained...

We answer a recent question of Bienvenu, Muchnik, Shen, and Vereshchagin. In particular, we prove an effective version of the standard fact from analysis which says that, for any ε > 0 and any Lebesgue-measurable subset of Cantor space, X ⊆ 2, there is an open set Uε ⊆ 2, Uε ⊇ X, such that μ(Uε) ≤ μ(X) + ε, where μ(Z) denotes the Lebesgue measure of Z ⊆ 2. More specifically, our main result sho...

In this note, we introduce a guiding principle to define topologies for a wide variety of spaces built from existing topological spaces. The topologies so-constructed will have a universal property taking one of two forms. If the topology is the coarsest so that a certain condition holds, we will give an elementary characterization of all continuous functions taking values in this new space. Al...