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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