Theorem retopn

Description: The topology of the real numbers. (Contributed by Thierry Arnoux, 30-Jun-2019)

	Ref	Expression
Assertion	retopn	|- ( topGen ` ran (,) ) = ( TopOpen ` RRfld )

Proof

Step	Hyp	Ref	Expression
1		eqid	|- ( TopOpen ` CCfld ) = ( TopOpen ` CCfld )
2	1	tgioo2	|- ( topGen ` ran (,) ) = ( ( TopOpen ` CCfld ) |`t RR )
3		df-refld	|- RRfld = ( CCfld |`s RR )
4	3 1	resstopn	|- ( ( TopOpen ` CCfld ) |`t RR ) = ( TopOpen ` RRfld )
5	2 4	eqtri	|- ( topGen ` ran (,) ) = ( TopOpen ` RRfld )