Is (2, 3) a Closed Set in the Phase Space X = [0, 1] ∪ (2, 3)?

[burak100]

X = [0, 1] \bigcup (2,3) is phase space.

Show that (2, 3) open and closed set of X .

the question is like that but I think it is false because it is not close, right?

 

[HallsofIvy]

I'm not sure what "phase space" has to do with this. This is a general topology question.

What makes you think it is not closed? What limit point of the set is there that is not in the set?

(Be very, very careful about the points 2 and 3!)

 

[burak100]

is it true?
Limit point of (2, 3) ---> again (2, 3) in X. then (2, 3) is closed in X.