Theorem topnfn

Description: The topology extractor function is a function on the universe. (Contributed by Mario Carneiro, 13-Aug-2015)

	Ref	Expression
Assertion	topnfn	$$⊢\mathrm{TopOpen}Fn\mathrm{V}$$

Proof

Step	Hyp	Ref	Expression
1		ovex	$$⊢\mathrm{TopSet}\left(w\right){\upharpoonright }_{𝑡}{\mathrm{Base}}_w\in \mathrm{V}$$
2		df-topn	$$⊢\mathrm{TopOpen}=\left(w\in \mathrm{V}⟼\mathrm{TopSet}\left(w\right){\upharpoonright }_{𝑡}{\mathrm{Base}}_w\right)$$
3	1 2	fnmpti	$$⊢\mathrm{TopOpen}Fn\mathrm{V}$$