Interior, Closure, Boundary and Cluster Points of a Set

[LauraLovies]

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.

 

[hgfalling]

The first three are right. Better review your definition of a limit point, though.

 

[LauraLovies]

any suggestions? a limit or cluster point is where a sequence converges...would it converge to 1 or the whole set?

 

[micromass]

To what possible points can a sequence in [0,1[ converge?

 

[LauraLovies]

to any point within the set?

 

[micromass]

Yes, so any point of [0,1[ are limit points.
Are there other points to which a sequence may converge?

 

[LauraLovies]

i am sure there are other points outside of the set which are limit points for sequences in the set

 

[micromass]

So, which points?

 

[LauraLovies]

im not really sure...maybe the complement of the set?