Separating near points

1. What is a separating set in graph theory?
2. Who introduced the separation point concept?
3. What does separated mean in math?

What is a separating set in graph theory?

In mathematics a set of functions S from a set D to a set C is called a separating set for D or said to separate the points of D if for any two distinct elements x and y of D, there exists a function f in S so that f(x) ≠ f(y).

Who introduced the separation point concept?

The concept was described by G. B. Halsted at the outset of his Synthetic Projective Geometry: With regard to a pair of different points of those on a straight, all remaining fall into two classes, such that every point belongs to one and only one.

What does separated mean in math?

In topology and related branches of mathematics, separated sets are pairs of subsets of a given topological space that are related to each other in a certain way: roughly speaking, neither overlapping nor touching.