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 = ∪ ( TopOpen ‘ ℂfld )

Proof

Step	Hyp	Ref	Expression
1		eqid	⊢ ( TopOpen ‘ ℂfld ) = ( TopOpen ‘ ℂfld )
2	1	cnfldtopon	⊢ ( TopOpen ‘ ℂfld ) ∈ ( TopOn ‘ ℂ )
3	2	toponunii	⊢ ℂ = ∪ ( TopOpen ‘ ℂfld )