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Definition df-brsiga 34183
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 34182 . 2 class 𝔅
2 cioo 13387 . . . . 5 class (,)
32crn 5686 . . . 4 class ran (,)
4 ctg 17482 . . . 4 class topGen
53, 4cfv 6561 . . 3 class (topGen‘ran (,))
6 csigagen 34139 . . 3 class sigaGen
75, 6cfv 6561 . 2 class (sigaGen‘(topGen‘ran (,)))
81, 7wceq 1540 1 wff 𝔅 = (sigaGen‘(topGen‘ran (,)))
Colors of variables: wff setvar class
This definition is referenced by:  brsiga  34184  brsigarn  34185  unibrsiga  34187  elmbfmvol2  34269  dya2iocbrsiga  34277  dya2icobrsiga  34278  sxbrsiga  34292  rrvadd  34454  rrvmulc  34455  orrvcval4  34467  orrvcoel  34468  orrvccel  34469
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