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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 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ccmp 20450 |
. 2
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2 | vx |
. . . . . . . 8
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3 | 2 | cv 1454 |
. . . . . . 7
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4 | 3 | cuni 4212 |
. . . . . 6
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5 | vy |
. . . . . . . 8
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6 | 5 | cv 1454 |
. . . . . . 7
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7 | 6 | cuni 4212 |
. . . . . 6
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8 | 4, 7 | wceq 1455 |
. . . . 5
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9 | vz |
. . . . . . . . 9
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10 | 9 | cv 1454 |
. . . . . . . 8
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11 | 10 | cuni 4212 |
. . . . . . 7
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12 | 4, 11 | wceq 1455 |
. . . . . 6
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13 | 6 | cpw 3963 |
. . . . . . 7
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14 | cfn 7595 |
. . . . . . 7
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15 | 13, 14 | cin 3415 |
. . . . . 6
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16 | 12, 9, 15 | wrex 2750 |
. . . . 5
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17 | 8, 16 | wi 4 |
. . . 4
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18 | 3 | cpw 3963 |
. . . 4
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19 | 17, 5, 18 | wral 2749 |
. . 3
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20 | ctop 19966 |
. . 3
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21 | 19, 2, 20 | crab 2753 |
. 2
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22 | 1, 21 | wceq 1455 |
1
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Colors of variables: wff setvar class |
This definition is referenced by: iscmp 20452 |
Copyright terms: Public domain | W3C validator |