Interior and closure in non-Euclidean topology

[tomkoolen]

Hello everyone,

I was wondering if someone could assist me with the following problem:

Let T be the topology on R generated by the topological basis B:
B = {{0}, (a,b], [c,d)}
a < b </ 0
0 </ c < d

Compute the interior and closure of the set A:
A = (−3, −2] ∪ (−1, 0) ∪ (0, 1) ∪ (2, 3)

I understand that in Euclidean topology I would just include/exclude the boundary points but I don't know how to do this with a different topology, especially since I feel that this topological space is very, very similar to the Euclidean topology, I have shown that all opens in that space are open here as well. What do I do?

Thanks in advance!

 

[Svein]

a < b </ 0
0 </ c < d

Do you mean a < b ≤ 0; 0 ≤ c < d?

 

[tomkoolen]

Yes!

 

[Svein]

The the problem must be dealt with in stages:

1. a < b < -3; 3 < c < d
2. a < -3, -3 < b <-2; 3 < c < d
3. etc. etc.