separation-theorems.txt

1 T0
2 T1
3 T2 (Hausdorff)
4 T2.5 (Completely Hausdorff)
5 T3
6 T3.5
7 T4
8 T5
9 Urysohn
10 Semiregular
11 Regular
12 Completely regular
13 Normal
14 Completely normal
15 Perfectly normal

Regular is equivalent to T0 and T3
@ -11 1
@ -11 5
@ -1 -5 11

Normal is equivalent to T4 and T1
@ -13 2
@ -13 7
@ -2 -7 13

Completely normal is equivalent to T5 and T1
@ -14 2
@ -14 8
@ -2 -8 14

Completely regular is equivalent to T3.5 and T0
@ -12 1
@ -12 6
@ -1 -6 12

T5 implies T4
@ -8 7

T4 and T3 implies T3.5
@ -5 -7 6

Normal implies T3.5
@ -13 6

T3.5 implies T3
@ -6 5

Completely normal implies Normal
@ -14 13

Regular implies T2.5
@ -11 4

T3 and T2 imply T2.5
@ -3 -5 4

T2.5 implies T2
@ -4 3

T2 implies T1
@ -3 2

T1 implies T0
@ -2 1

Perfectly normal implies Completely normal
@ -15 14

Completely normal implies Normal
@ -14 13

Normal implies T3.5
@ -13 6

T3.5 implies Urysohn
@ -6 9

T3.5 implies Regular
@ -6 11

Urysohn implies T2.5
@ -9 4

Urysohn implies Semiregular
@ -9 10

Semiregular implies T2
@ -10 3