Theorem xrtgioo2

Description: The topology on the extended reals coincides with the standard topology on the reals, when restricted to RR . (Contributed by Glauco Siliprandi, 5-Feb-2022)

	Ref	Expression
Assertion	xrtgioo2	⊢ ( topGen ‘ ran (,) ) = ( ( ordTop ‘ ≤ ) ↾t ℝ )

Proof

Step	Hyp	Ref	Expression
1		eqid	⊢ ( ( ordTop ‘ ≤ ) ↾t ℝ ) = ( ( ordTop ‘ ≤ ) ↾t ℝ )
2	1	xrtgioo	⊢ ( topGen ‘ ran (,) ) = ( ( ordTop ‘ ≤ ) ↾t ℝ )