Neutrosophy consists of neutrosophic logic, probability, and sets. Actually, the neutrosophic set is a generalisation of classical sets, fuzzy set, intuitionistic fuzzy set, etc. A neutrosophic set is a mathematical notion serving issues containing inconsistent, indeterminate, and imprecise data. The notion of intuitionistic fuzzy metric space is useful in modelling some phenomena where it is necessary to study the relationship between two probability functions. In this paper, the definition of new metric space with neutrosophic numbers is given. Neutrosophic metric space uses the idea of continuous triangular norms and continuous triangular conorms in intuitionistic fuzzy metric space. Triangular norms are used to generalize with the probability distribution of triangle inequality in metric space conditions. Triangular conorms are known as dual operations of triangular norms. Triangular norms and triangular conorm are very significant for fuzzy operations. Neutrosophic metric space was defined with continuous triangular norms and continuous triangular conorms. Several topological and structural properties neutrosophic metric space have been investigated. The analogues of Baire Category Theorem and Uniform Convergence Theorem are given for Neutrosophic metric spaces.

中文翻译：

---

中智度量空间

中智学由中智逻辑，概率和集合组成。实际上，中智集是对经典集，模糊集，直觉模糊集等的概括。中智集是一种数学概念，用于解决包含不一致，不确定和不精确数据的问题。直觉模糊度量空间的概念在某些现象的建模中很有用，在这种现象中有必要研究两个概率函数之间的关系。在本文中，给出了带有中智数的新度量空间的定义。中智度量空间使用直觉模糊度量空间中的连续三角形范数和连续三角形范数的思想。三角形范数用于度量空间条件下三角形不等式的概率分布。三角定理被称为三角范数的对偶运算。三角范数和三角范数对于模糊运算非常重要。中智度量空间定义为连续的三角形范数和连续的三角形锥范。已经研究了中智度量空间的几种拓扑和结构特性。对于中智度量空间，给出了Baire类定理和一致收敛定理的类似物。