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 RR )

Proof

Step Hyp Ref Expression
1 eqid
 |-  ( ( ordTop ` <_ ) |`t RR ) = ( ( ordTop ` <_ ) |`t RR )
2 1 xrtgioo
 |-  ( topGen ` ran (,) ) = ( ( ordTop ` <_ ) |`t RR )