Theorem retop

Description: The standard topology on the reals. (Contributed by FL, 4-Jun-2007)

	Ref	Expression
Assertion	retop	$$⊢\mathrm{topGen}\left(\mathrm{ran}\left(.\right)\right)\in \mathrm{Top}$$

Proof

Step	Hyp	Ref	Expression
1		retopbas	$$⊢\mathrm{ran}\left(.\right)\in \mathrm{TopBases}$$
2		tgcl	$$⊢\mathrm{ran}\left(.\right)\in \mathrm{TopBases}\to \mathrm{topGen}\left(\mathrm{ran}\left(.\right)\right)\in \mathrm{Top}$$
3	1 2	ax-mp	$$⊢\mathrm{topGen}\left(\mathrm{ran}\left(.\right)\right)\in \mathrm{Top}$$