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Mirrors > Home > MPE Home > Th. List > df-t0 | Structured version Visualization version Unicode version |
Description: Define T0 or Kolmogorov spaces. A T0 space satisfies a kind of "topological extensionality" principle (compare ax-ext 2602): any two points which are members of the same open sets are equal, or in contraposition, for any two distinct points there is an open set which contains one point but not the other. This differs from T1 spaces (see ist1-2 21151) in that in a T1 space you can choose which point will be in the open set and which outside; in a T0 space you only know that one of the two points is in the set. (Contributed by Jeff Hankins, 1-Feb-2010.) |
Ref | Expression |
---|---|
df-t0 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ct0 21110 | . 2 | |
2 | vx | . . . . . . . . 9 | |
3 | vo | . . . . . . . . 9 | |
4 | 2, 3 | wel 1991 | . . . . . . . 8 |
5 | vy | . . . . . . . . 9 | |
6 | 5, 3 | wel 1991 | . . . . . . . 8 |
7 | 4, 6 | wb 196 | . . . . . . 7 |
8 | vj | . . . . . . . 8 | |
9 | 8 | cv 1482 | . . . . . . 7 |
10 | 7, 3, 9 | wral 2912 | . . . . . 6 |
11 | 2, 5 | weq 1874 | . . . . . 6 |
12 | 10, 11 | wi 4 | . . . . 5 |
13 | 9 | cuni 4436 | . . . . 5 |
14 | 12, 5, 13 | wral 2912 | . . . 4 |
15 | 14, 2, 13 | wral 2912 | . . 3 |
16 | ctop 20698 | . . 3 | |
17 | 15, 8, 16 | crab 2916 | . 2 |
18 | 1, 17 | wceq 1483 | 1 |
Colors of variables: wff setvar class |
This definition is referenced by: ist0 21124 |
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