Metamath Proof Explorer


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 )