Theorem letopon

Description: The topology of the extended reals. (Contributed by Mario Carneiro, 3-Sep-2015)

	Ref	Expression
Assertion	letopon	$$⊢\mathrm{ordTop}\left(\le \right)\in \mathrm{TopOn}\left({ℝ}^{*}\right)$$

Proof

Step	Hyp	Ref	Expression
1		letsr	$$⊢\le \in \mathrm{TosetRel}$$
2		ledm	$$⊢{ℝ}^{*}=\mathrm{dom}\le$$
3	2	ordttopon	$$⊢\le \in \mathrm{TosetRel}\to \mathrm{ordTop}\left(\le \right)\in \mathrm{TopOn}\left({ℝ}^{*}\right)$$
4	1 3	ax-mp	$$⊢\mathrm{ordTop}\left(\le \right)\in \mathrm{TopOn}\left({ℝ}^{*}\right)$$