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Definition df-brsiga 30068
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, (sigaGen‘𝐽), so there is no need to introduce a special constant function for Borel sigma-algebra. (Contributed by Thierry Arnoux, 27-Dec-2016.)
Assertion
Ref Expression
df-brsiga 𝔅 = (sigaGen‘(topGen‘ran (,)))

Detailed syntax breakdown of Definition df-brsiga
StepHypRef Expression
1 cbrsiga 30067 . 2 class 𝔅
2 cioo 12133 . . . . 5 class (,)
32crn 5085 . . . 4 class ran (,)
4 ctg 16038 . . . 4 class topGen
53, 4cfv 5857 . . 3 class (topGen‘ran (,))
6 csigagen 30024 . . 3 class sigaGen
75, 6cfv 5857 . 2 class (sigaGen‘(topGen‘ran (,)))
81, 7wceq 1480 1 wff 𝔅 = (sigaGen‘(topGen‘ran (,)))
Colors of variables: wff setvar class
This definition is referenced by:  brsiga  30069  brsigarn  30070  unibrsiga  30072  elmbfmvol2  30152  dya2iocbrsiga  30160  dya2icobrsiga  30161  sxbrsiga  30175  rrvadd  30337  rrvmulc  30338  orrvcval4  30349  orrvcoel  30350  orrvccel  30351
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