Neutrosophic Bitopological Spaces

WOS: 000502521500006In this study, bitopological structure which is a more general structure than topological spaces is built on neutrosophic sets. The necessary arguments which are pairwise neutrosophic open set, pairwise neutrosophic closed set, pairwise neutrosophic closure, pairwise neutrosophic interior are defined and their basic properties are presented. The relations of these concepts with their counterparts in neutrosophic topological spaces are given and many examples are presented

Functorial comparisons of bitopology with topology and the case for redundancy of bitopology in lattice-valued mathematics

[EN] This paper studies various functors between (lattice-valued) topology and (lattice-valued) bitopology, including the expected “doubling” functor Ed : L-Top → L-BiTop and the “cross” functor E× : L-BiTop → L2-Top introduced in this paper, both of which are extremely well-behaved strict, concrete, full embeddings. Given the greater simplicity of lattice-valued topology vis-a-vis lattice-valued bitopology and the fact that the class of L2-Top’s is strictly smaller than the class of L-Top’s encompassing fixed-basis topology, the class of E×’s makes the case that lattice-valued bitopology is categorically redundant. As a special application, traditional bitopology as represented by BiTop is (isomorphic in an extremely well-behaved way to) a strict subcategory of 4-Top, where 4 is the four element Boolean algebra; this makes the case that traditional bitopology is a special case of a much simpler fixed-basis topology.Support of Youngstown State University via a sabbatical for the 2005–2006 academic year is gratefully acknowledged.Rodabaugh, S. (2008). Functorial comparisons of bitopology with topology and the case for redundancy of bitopology in lattice-valued mathematics. Applied General Topology. 9(1):77-108. doi:10.4995/agt.2008.1871.SWORD771089

The Lattice of Intuitionistic Fuzzy Topologies Generated by Intuitionistic Fuzzy Relations

We generalize the notion of fuzzy topology generated by fuzzy relation given by Mishra and Srivastava to the setting of intuitionistic fuzzy sets. Some fundamental properties and necessary examples are given. More specifically, we provide the lattice structure to a family of intuitionistic fuzzy topologies generated by intuitionistic fuzzy relations. To that end, we study necessary structural characteristics such as distributivity, modularity and complementary of this lattice

Sequentially dinormal ditopological texture spaces and dimetrizability

AbstractThe authors extend the bitopological notion of sequential normality to ditopological texture spaces, and use this notion to state and prove a (pseudo-)dimetrizability theorem

A note on the algebra of triple sets

In this paper, we introduce the notion of triple sets. They can be considered as a bridge between double and intuitionistic sets or as their specific combination. Triple sets have some features of both these classes and thus they are able to model two aspects of uncertainty. On the one hand, they express the modal idea of necessity and possibility. On the other, they refer to the fact that while some objects may be accepted by decision maker (that is, considered as being true) and some can be rejected (thus treated as false), is is still possible that there are some neutral objects. We define some basic algebraic operations on triple sets and analyze their properties (comparing them e.g. with intuitionistic logic). We compare two approaches to the notion of complement (negation in the logical sense). We point out that some natural extensions of this framework should be studied to

On the Topology Induced by C*-Algebra-Valued Fuzzy Metric Spaces

We define the notion of C * -algebra-valued fuzzy metric spaces and we study the topology induced by these spaces.The authors are grateful to the Basque Government by the support, of this work through Grant IT1207-19

Some categorical aspects of the inverse limits in ditopological context

[EN] This paper considers some various categorical aspects of the inverse systems (projective spectrums) and inverse limits described in the category ifPDitop, whose objects are ditopological plain texture spaces and morphisms are bicontinuous point functions satisfying a compatibility condition between those spaces. In this context, the category InvifPDitop consisting of the inverse systems constructed by the objects and morphisms of ifPDitop, besides the inverse systems of mappings, described between inverse systems, is introduced, and the related ideas are studied in a categorical - functorial setting. In conclusion, an identity natural transformation is obtained in the context of inverse systems - limits constructed in ifPDitop and the ditopological infinite products are characterized by the finite products via inverse limits.Yildiz, F. (2018). Some categorical aspects of the inverse limits in ditopological context. Applied General Topology. 19(1):101-127. https://doi.org/10.4995/agt.2018.781210112719