Metamath Proof Explorer


Definition df-brsiga

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 (,) ) )

Detailed syntax breakdown

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 (,) ) )