2 Euclidean topology

Question 1

Euclidean topology

Answer 1

A subset S of R(real) is said to be open in the euclidean topology on R if it has the following property:
For each x e S, there exist a,b in R, with a < b, such that x e (a,b) (_ S.

Question 2

Basis

Answer 2

Let (X, T) be a topological space. A collection B of open subsets of X is said to be a basis for the topology T if every open set is a union of members of B.