Question

What is the derived set S` of the set S={x: 0≤x<1}

Answer 1

Answer:

In mathematics, more specifically in point-set topology, the derived set of a subset S of a topological space is the set of all limit points of S. It is usually denoted by S '.

In mathematics, more specifically in point-set topology, the derived set of a subset S of a topological space is the set of all limit points of S. It is usually denoted by S '.The concept was first introduced by Georg Cantor in 1872 and he developed set theory in large part to study derived sets on the real line.

Answer 2

Answer:

It's clear that 0∈A′. Any neighbourhood of 0 contains all but finitely many of the 1n.

If x≠0 there is always a neighbourhood Ux of x such that A∩Ux={x} (if x∈A) or Ux∩A=∅.

This holds as any x>0 has possibly

two x−,x+∈A with x−<x<x+ such that (x−,x)∩A=∅ .

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