Theorem sn0top

Description: The singleton of the empty set is a topology. (Contributed by Stefan Allan, 3-Mar-2006) (Proof shortened by Mario Carneiro, 13-Aug-2015)

	Ref	Expression
Assertion	sn0top	$$⊢\left\{\varnothing \right\}\in \mathrm{Top}$$

Proof

Step	Hyp	Ref	Expression
1		sn0topon	$$⊢\left\{\varnothing \right\}\in \mathrm{TopOn}\left(\varnothing \right)$$
2	1	topontopi	$$⊢\left\{\varnothing \right\}\in \mathrm{Top}$$