Definition df-brsiga 34581

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	⊢ 𝔅ℝ = (sigaGen‘(topGen‘ran (,)))

Detailed syntax breakdown of Definition df-brsiga

Step	Hyp	Ref	Expression
1		cbrsiga 34580	. 2 class 𝔅ℝ
2		cioo 13376	. . . . 5 class (,)
3	2	crn 5662	. . . 4 class ran (,)
4		ctg 17494	. . . 4 class topGen
5	3, 4	cfv 6536	. . 3 class (topGen‘ran (,))
6		csigagen 34537	. . 3 class sigaGen
7	5, 6	cfv 6536	. 2 class (sigaGen‘(topGen‘ran (,)))
8	1, 7	wceq 1570	1 wff 𝔅ℝ = (sigaGen‘(topGen‘ran (,)))

This definition is used by:  brsiga  34582  brsigarn  34583  unibrsiga  34585  elmbfmvol2  34666  dya2iocbrsiga  34674  dya2icobrsiga  34675  sxbrsiga  34689  rrvadd  34851  rrvmulc  34852  orrvcval4  34864  orrvcoel  34865  orrvccel  34866