Measurement space and Density

Metric Space, also known as normed vector space, refers to a set in mathematics and the distance between any elements in the set is configurable. The most intuitive understanding of a measurement space is the three-dimensional Euclidean space. The Euclidean measure in this space defines the distance between two points as the length of the line connecting these two points.
Definition
Set X to a set, D: x → R. If any x, y, and z belong to X
(I) (Positive Definite) d (x, y) ≥0, and d (x, y) = 0 When and only when x = y;
(Ii) (Symmetry) d (x, y) = d (y, X );
(Iii) (triangular inequality) d (x, z) ≤ d (x, y) + d (y, z)
D is a measurement of X. The even pair (x, D) is a measurement space, or X is a measurement space for the measurement D.

Dense & distinct:
Explanation 1: If any point in B contains a point in any neighborhood, B is dense in. Or, the closure of B contains a and B is dense in.
If B is not dense in any opening sub-set of A, it is the shorang set.
Note: density and shorang are not two complementary concepts. Not dense. Shu Lang is not dense everywhere.

Explanation 2: A is dense in B, which means that any point in B can be approached by the vertex in a, just as the set of all polynomials is dense in the continuous function space.
However, the closure does not contain any interior point. It's like a consortium.
These two concepts are indeed related to the defined topology.

Explanation 3: taking rational data set as an example, you can also think like this: For any vertex a in a real number set, you can find a sequence in the rational number set with a as the limit.