Definition.
Let S be a subset of ℝ. A point x ∈ ℝ is said to be an adherent point of S if every neighbourhood of x contains a point of S. It follows that x is an adherent point of S if N(x,ε )∩S ≠Φ for every ε>0.
The set of all adherent points of S is said to be the closure of S and is denoted by S̅. From the definition, it follows that S⊂ S̅ for any set S⊂ℝ.
0 Comments