In this paper, we introduce topological notions defined by means of β-open sets when these are planted into the framework of Ying’s fuzzifying topological spaces (by Lukasiewicz logic in [0, 1]).We introduce T 0 β -; T 1 β -; T 2 β - (β- Hausdorff)-, T 3 β - (β-regular)- and T 4 β - (β-normal)-separation axioms. Furthermore, the R 0 β - and R 1 β - separation axioms are studied and their relations with the T 1 β - and  T 2 β - separation axioms are introduced. Moreover, we clarify the relations of these axioms with each other as well as the relations with other fuzzifying separation axioms.

This paper considers fuzzifying topologies, a special case of I -fuzzy topologies (bifuzzy topologies), introduced by Ying [1]. It investigates topological notions defined by means of α-open sets when these are planted into the framework of Ying’s fuzzifying topological spaces (by Lukasiewicz logic in [0, 1]) . The concept of α-irresolute functions and α-compactness in the framework of fuzzifying topology are introduced and some of their properties are obtained. We use the finite intersection property to give a characterization of fuzzifying α-compact spaces. Furthermore, we study the image of fuzzifying α-compact
spaces under fuzzifying α-continuity and fuzzifying α-irresolute maps.

@ 2012 Egyptian Mathematical Society.

This paper considers fuzzifying topologies, a special case of I-fuzzy topologies (bifuzzy topologies), introduced by Ying [25]. It investigates topological notions defined by means of D -open sets when these are planted into the framework of Ying’s fuzzifying topological spaces (by Łukasiewicz logic in [0, 1]). In this paper we introduce some sorts of operations, called general fuzzifying operations from P(X) to Á(X) , where (X,t) is a fuzzifying topological space. By making use of them we contract neighborhood structures, derived sets, closure operations and

interior operations. © 2012 SciRes. 

Doi:10.4236/am.2012.39146

In this paper, supra β-connectedness are researched by means of a supra β- separated sets. © Pakistan Academy of Sciences
 

From quasi t-norms and quasi t-conorms we give methods to generate new quasi t-norms and new quasi-t-conorms. Furthermore, between ∧ (resp. ∨) and every quasi t-norm (resp. quasi t-conorm) f (resp. f^*) it is proved the existence of finite sequences of quasi t-norms (resp. quasi t-conorms) lies between ∧ (resp. ∨) and f (resp. f^*). Finally, we give some special cases of complete residuated lattice valued-logic.

In this paper, a new class of sets and maps between topological spaces called supra pre-open sets and supra pre-continuous maps, respectively are introduced and studied. Furthermore, the concepts of supra pre-open maps and supra pre-closed maps in terms of supra pre-open sets and supra pre-closed sets, respectively, are introduced and several properties of them are investigated.

In (2010) Sayed and Noiri [1], introduced and investigated a class of sets and maps between topological spaces called supra b-open sets and supra b-continuous maps, respectively. In this note, we show that Proposition 1 is incorrect.

 

In this paper, we introduce and investigate a new class of sets and maps between topological spaces called supra b-open sets and supra b-continuous maps, respectively. Furthermore, we introduce the concepts of supra b-open maps and supra bclosed maps and investigate several properties of them.

Undoped and (Ni, Co, and Mn)-doped ZnS nanoparticles (NPs) are successfully synthesized by a  sonochemical assisted co-precipitation technique. XRD patterns reveal the incorporation of dopant ions by substitution of Zn
ions. Ni ions induce growth rate enhancement and the increase of crystallite size, whereas Co and Mn ions slow
down the growth rate and caused the decrease of the corresponding crystallite size. The UV–visible absorption
spectra exhibit a decrease in the optical band gap for all doped samples. The photoluminescence spectra of Co and Mn-doped ZnS NPs show an improvement in the visible light, whereas Ni-doping results in a slight decrease
in the emission intensity allover the spectral range. The room-temperature ferromagnetism of ZnS NPs is strongly
improved by Ni- and Co-doping and slightly enhanced by Mn-doping. The AC conductivity of ZnS NPS is
enhanced by Ni- and Co-doping and decreased by Mn-doping in the frequency range from 2 kHz to 1 MHz.