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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 )