Topology greatly benefits from the concept of δ-cloure. Its quiet nature to extended its proper-ties in other topological spaces. So, with the concept of quasi-coincidence Ganguly and Saha pioneered ...and extensively examined the notion of δ-closure within the domain of fuzzy topological spaces (FTS). The theory of δ-closure in intuitionistic fuzzy topological spaces (IFTS) was further extended by Seok Jong Lee and Yeon Seok Eom. In this work, the notion of Nδ-closure in Neutrosophic Topological Spaces (NTS) is put forward and discussed.
Soft ω-local indiscreetness as a weaker form of both soft local countability and soft local indiscreetness is introduced. Then soft ω-regularity as a weaker form of both soft regularity and soft ...ω-local indiscreetness is defined and investigated. Additionally, soft ω-T2 as a new soft topological property that lies strictly between soft T2 and soft T1 is defined and investigated. It is proved that soft anti-local countability is a sufficient condition for equivalence between soft ω-locally indiscreetness (resp. soft ω-regularity) and soft locally indiscreetness (resp. soft ω-regularity). Additionally, it is proved that the induced topological spaces of a soft ω-locally indiscrete (resp. soft ω-regular, soft ω-T2) soft topological space are (resp. ω-regular, ω-T2) topological spaces. Additionally, it is proved that the generated soft topological space of a family of ω-locally indiscrete (resp. ω-regular, ω-T2) topological spaces is soft ω-locally indiscrete and vice versa. In addition to these, soft product theorems regarding soft ω-regular and soft ω-T2 soft topological spaces are obtained. Moreover, it is proved that soft ω-regular and soft ω-T2 are hereditarily under soft subspaces.
For a wide category K, we introduce the notions of a K-precomplete map and of a K-subspace. Based on these, we create a uniform method for constructing K-completions of T.sub.0-spaces.
We present a family of hypersurfaces of revolution distinguished by four parameters in the five-dimensional pseudo-Euclidean space Esub.2 sup.5 . The matrices corresponding to the fundamental form, ...Gauss map, and shape operator of this family are computed. By utilizing the Cayley–Hamilton theorem, we determine the curvatures of the specific family. Furthermore, we establish the criteria for maximality within this framework. Additionally, we reveal the relationship between the Laplace–Beltrami operator of the family and a 5×5 matrix.
In this paper, we consider canonical F-planar mappings of spaces with affine connection onto m-symmetric spaces. We obtained the fundamental equations of these mappings in the form of a closed system ...of Chauchy-type equations in covariant derivatives. Furthermore, we established the number of essential parameters on which its general solution depends.
This paper defines the so-called pairwise r-compactness in topological and bitopological spaces. In particular, several inferred properties of the r-compact spaces and their connections with other ...topological and bitopological spaces are studied theoretically. As a result, several novel theorems of the r-compact space are generalized on the pairwise r-compact space. The results established in this research paper are new in the field of topology.
In this paper, we study the space of G-permutation degree of some classes of topological spaces and the properties of the functor SPsub.G sup.n of G-permutation degree. In particular, we prove: (a) ...If a topological space X is developable, then so is SPsub.G sup.n X; (b) If X is a Moore space, then so is SPsub.G sup.n X; (c) If a topological space X is an Msub.1 -space, then so is SPsub.G sup.n X; (d) If a topological space X is an Msub.2 -space, then so is SPsub.G sup.n X.
This manuscript comes as first attempt in building a new type of neutrosophic topological spaces, the aim is to shed the light on a new structure known as the n.sup.th-power set P.sup.n{X) of a set, ...this new kind of sets enables authors to create and built new topology spaces called Neutrosophic SuperHyper Topological Spaces and Neutrosophic SuperHyper Bi-Topological Spaces , the n.sup.th-power sets are the optimal representation for the applications in our real world. In this article, new concepts and theorems related to this new topologies have been discussed, which are pairwise neutrosophic open n.sup.th -power set, pairwise neutrosophic closed n.sup.th -power set, as well as, the closures and the interiors are defined with their properties. Many of relations for these concepts have been introduced. Keywords: n.sup.th -power set P.sup.n{X) ; Neutrosophic SuperHyper Topological Spaces (NSHTSs); Neutrosophic SuperHyper Bi-Topological Spaces (NSHBi-TSs).
Fibrewise soft ideal topological space Yousif, Yousif Y; Ghafel, Mohammed A H
Journal of physics. Conference series,
05/2018, Letnik:
1003, Številka:
1
Journal Article
Recenzirano
Odprti dostop
In this work we explain and discuss new notion of fibrewise topological spaces, called fibrewise soft ideal topological spaces, Also, we show the notions of fibrewise closed soft ideal topological ...spaces, fibrewise open soft ideal topological spaces and fibrewise soft near ideal topological spaces.
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