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Definition df-brsiga 33478
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 33477 . 2 class 𝔅
2 cioo 13328 . . . . 5 class (,)
32crn 5676 . . . 4 class ran (,)
4 ctg 17387 . . . 4 class topGen
53, 4cfv 6542 . . 3 class (topGen‘ran (,))
6 csigagen 33434 . . 3 class sigaGen
75, 6cfv 6542 . 2 class (sigaGen‘(topGen‘ran (,)))
81, 7wceq 1539 1 wff 𝔅 = (sigaGen‘(topGen‘ran (,)))
Colors of variables: wff setvar class
This definition is referenced by:  brsiga  33479  brsigarn  33480  unibrsiga  33482  elmbfmvol2  33564  dya2iocbrsiga  33572  dya2icobrsiga  33573  sxbrsiga  33587  rrvadd  33749  rrvmulc  33750  orrvcval4  33761  orrvcoel  33762  orrvccel  33763
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