Description: A Borel Algebra is defined as a sigma-algebra generated by a topology. 'The' Borel sigma-algebra here refers to the sigma-algebra generated by the topology of open intervals on real numbers. The Borel algebra of a given topology J is the sigma-algebra generated by J , ( sigaGenJ ) , so there is no need to introduce a special constant function for Borel sigma-algebra. (Contributed by Thierry Arnoux, 27-Dec-2016)
Ref | Expression | ||
---|---|---|---|
Assertion | df-brsiga | |- BrSiga = ( sigaGen ` ( topGen ` ran (,) ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
0 | cbrsiga | |- BrSiga |
|
1 | csigagen | |- sigaGen |
|
2 | ctg | |- topGen |
|
3 | cioo | |- (,) |
|
4 | 3 | crn | |- ran (,) |
5 | 4 2 | cfv | |- ( topGen ` ran (,) ) |
6 | 5 1 | cfv | |- ( sigaGen ` ( topGen ` ran (,) ) ) |
7 | 0 6 | wceq | |- BrSiga = ( sigaGen ` ( topGen ` ran (,) ) ) |