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Mathbox for Thierry Arnoux |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > df-pcmp | Structured version Visualization version GIF version |
Description: Definition of a paracompact topology. A topology is said to be paracompact iff every open cover has an open refinement that is locally finite. The definition 6 of [BourbakiTop1] p. I.69. also requires the topology to be Hausdorff, but this is dropped here. (Contributed by Thierry Arnoux, 7-Jan-2020.) |
Ref | Expression |
---|---|
df-pcmp | β’ Paracomp = {π β£ π β CovHasRef(LocFinβπ)} |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cpcmp 32493 | . 2 class Paracomp | |
2 | vj | . . . . 5 setvar π | |
3 | 2 | cv 1541 | . . . 4 class π |
4 | clocfin 22871 | . . . . . 6 class LocFin | |
5 | 3, 4 | cfv 6497 | . . . . 5 class (LocFinβπ) |
6 | 5 | ccref 32480 | . . . 4 class CovHasRef(LocFinβπ) |
7 | 3, 6 | wcel 2107 | . . 3 wff π β CovHasRef(LocFinβπ) |
8 | 7, 2 | cab 2710 | . 2 class {π β£ π β CovHasRef(LocFinβπ)} |
9 | 1, 8 | wceq 1542 | 1 wff Paracomp = {π β£ π β CovHasRef(LocFinβπ)} |
Colors of variables: wff setvar class |
This definition is referenced by: ispcmp 32495 |
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