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Mirrors > Home > MPE Home > Th. List > df-cmp | Structured version Visualization version Unicode version |
Description: Definition of a compact topology. A topology is compact iff any open covering of its underlying set contains a finite sub-covering (Heine-Borel property). Definition C''' of [BourbakiTop1] p. I.59. Note: Bourbaki uses the term quasi-compact topology but it is not the modern usage (which we follow). (Contributed by FL, 22-Dec-2008.) |
Ref | Expression |
---|---|
df-cmp |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ccmp 21189 | . 2 | |
2 | vx | . . . . . . . 8 | |
3 | 2 | cv 1482 | . . . . . . 7 |
4 | 3 | cuni 4436 | . . . . . 6 |
5 | vy | . . . . . . . 8 | |
6 | 5 | cv 1482 | . . . . . . 7 |
7 | 6 | cuni 4436 | . . . . . 6 |
8 | 4, 7 | wceq 1483 | . . . . 5 |
9 | vz | . . . . . . . . 9 | |
10 | 9 | cv 1482 | . . . . . . . 8 |
11 | 10 | cuni 4436 | . . . . . . 7 |
12 | 4, 11 | wceq 1483 | . . . . . 6 |
13 | 6 | cpw 4158 | . . . . . . 7 |
14 | cfn 7955 | . . . . . . 7 | |
15 | 13, 14 | cin 3573 | . . . . . 6 |
16 | 12, 9, 15 | wrex 2913 | . . . . 5 |
17 | 8, 16 | wi 4 | . . . 4 |
18 | 3 | cpw 4158 | . . . 4 |
19 | 17, 5, 18 | wral 2912 | . . 3 |
20 | ctop 20698 | . . 3 | |
21 | 19, 2, 20 | crab 2916 | . 2 |
22 | 1, 21 | wceq 1483 | 1 |
Colors of variables: wff setvar class |
This definition is referenced by: iscmp 21191 |
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