Consider the following topologies on the set R of all real numbers.
T1 is the upper limit topology having all sets (a, b] as basis.
T2 ={U ⊂ ℝ : ℝ\U is finite} ∪ {Ø}.
T3 is the standard topology having all sets (a, b) as basis. Then
1
T2 ⊂ T3 ⊂ T1
2
T1 ⊂ T2 ⊂ T3
3
T3 ⊂ T2 ⊂ T1
4
T2 ⊂ T1 ⊂ T3