Theorem tgioo4

Description: The standard topology on the reals is a subspace of the complex metric topology. (Contributed by Glauco Siliprandi, 5-Feb-2022)

	Ref	Expression
Assertion	tgioo4	$$⊢\mathrm{topGen}\left(\mathrm{ran}\left(.\right)\right)=\mathrm{TopOpen}\left({ℂ}_{\mathrm{fld}}\right){\upharpoonright }_{𝑡}ℝ$$

Proof

Step	Hyp	Ref	Expression
1		eqid	$$⊢\mathrm{TopOpen}\left({ℂ}_{\mathrm{fld}}\right)=\mathrm{TopOpen}\left({ℂ}_{\mathrm{fld}}\right)$$
2	1	tgioo2	$$⊢\mathrm{topGen}\left(\mathrm{ran}\left(.\right)\right)=\mathrm{TopOpen}\left({ℂ}_{\mathrm{fld}}\right){\upharpoonright }_{𝑡}ℝ$$