Theorem unicntop

Description: The underlying set of the standard topology on the complex numbers is the set of complex numbers. (Contributed by Glauco Siliprandi, 11-Dec-2019)

	Ref	Expression
Assertion	unicntop	$$⊢ℂ=\bigcup \mathrm{TopOpen}\left({ℂ}_{\mathrm{fld}}\right)$$

Proof

Step	Hyp	Ref	Expression
1		eqid	$$⊢\mathrm{TopOpen}\left({ℂ}_{\mathrm{fld}}\right)=\mathrm{TopOpen}\left({ℂ}_{\mathrm{fld}}\right)$$
2	1	cnfldtopon	$$⊢\mathrm{TopOpen}\left({ℂ}_{\mathrm{fld}}\right)\in \mathrm{TopOn}\left(ℂ\right)$$
3	2	toponunii	$$⊢ℂ=\bigcup \mathrm{TopOpen}\left({ℂ}_{\mathrm{fld}}\right)$$