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Interior, Closure, Boundary and Cluster Points of a Set

  • #1

Homework Statement


Find the closure, interior, boundary and limit points of the set [0,1)


Homework Equations





The Attempt at a Solution



I think that the closure is [0,1]. I believe the interior is (0,1) and the boundary are the points 0 and 1. I think the limit point may also be 0. I do not know, however, if I am on the right track.
 

Answers and Replies

  • #2
351
1
The first three are right. Better review your definition of a limit point, though.
 
  • #3
any suggestions? a limit or cluster point is where a sequence converges...would it converge to 1 or the whole set?
 
  • #4
22,097
3,282
To what possible points can a sequence in [0,1[ converge?
 
  • #5
to any point within the set?
 
  • #6
22,097
3,282
Yes, so any point of [0,1[ are limit points.
Are there other points to which a sequence may converge?
 
  • #7
i am sure there are other points outside of the set which are limit points for sequences in the set
 
  • #8
22,097
3,282
So, which points?
 
  • #9
im not really sure...maybe the complement of the set?
 

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