Abstract
In this paper, we develop the notion of the basis for a smooth neutrosophic topology in a more natural way. As a sequel, we define the notion of symmetric neutrosophic quasi-coincident neighborhood systems and prove some interesting results that fit with the classical ones, to establish the consistency of theory developed. Finally, we define and discuss the concept of product topology, in this context, using the definition of basis.
Highlights
The idea of neutrosophy was initiated and developed by Smarandache [1] in 1999
Šostak [8] observed that Chang’s approach is crisp in nature and so he redefined the notion of fuzzy topology, often referred as smooth fuzzy topology, as a function from the collection of all fuzzy subsets of X to [0, 1]; Fang Jin-ming et al and Vembu et al [9,10] are some who discussed the concept of basis as a function from a suitable collection of fuzzy subsets of X to [0, 1]
Symmetry 2020, 12, 1557 and subbasis for a smooth neutrosophic topology; further, we develop the theory using the concept of neutrosophic quasi-coincident neighborhood systems
Summary
The idea of neutrosophy was initiated and developed by Smarandache [1] in 1999. In recent decades the theory was used at various junctions of mathematics. Wang, Nanjing, Liang and Yan [11,12] developed a parallel theory in the context of intuitionistic I-fuzzy topological spaces. The notion of the basis for an ordinary single-valued neutrosophic topology was defined and discussed by Kim [15]. Alblowi, Shumrani, Muhammed Gulisten, Smarandache, Saber, Alsharari, Zhang and Sunderraman [4,16,17] are some others who posted their work in the context of single-valued neutrosophic topological spaces.
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