• Support PF! Buy your school textbooks, materials and every day products Here!

Interior of a Set

  • Thread starter Piglet1024
  • Start date
  • #1
I have to describe the interior of the subsets of R: Z,Q.

I don't understand how to tell if these certain subsets are open or how to tell what the interior is, can someone please explain
 

Answers and Replies

  • #2
211
0
Are you working with the standard open-ball topology on the real line?

If so, then a point [itex]p \in S \subset \mathbb{R}[/itex] is an interior point of S if for some [itex]\epsilon >0[/itex], the open interval [itex](p-\epsilon, p+\epsilon)[/itex] lies completely inside. In other words, a point is an interior point if it lies in the set and is not a boundary point of the set.

For example, 2 is an interior point of [1,4], but 1 is not an interior point (on the boundary) and neither is 0 (not in the set).

What happens when you draw a small open interval around a rational number? Will that interval lie completely inside the rational numbers, or does it contain an irrational number?
 

Related Threads on Interior of a Set

  • Last Post
Replies
4
Views
725
  • Last Post
Replies
4
Views
2K
  • Last Post
Replies
2
Views
4K
  • Last Post
Replies
2
Views
551
  • Last Post
Replies
4
Views
2K
  • Last Post
Replies
6
Views
8K
Replies
3
Views
285
Replies
2
Views
1K
Replies
8
Views
2K
Replies
18
Views
3K
Top