Theorem xrge0topn

Description: The topology of the extended nonnegative real numbers. (Contributed by Thierry Arnoux, 20-Jun-2017)

	Ref	Expression
Assertion	xrge0topn	⊢ ( TopOpen ‘ ( ℝ*𝑠 ↾s ( 0 [,] +∞ ) ) ) = ( ( ordTop ‘ ≤ ) ↾t ( 0 [,] +∞ ) )

Proof

Step	Hyp	Ref	Expression
1		eqid	⊢ ( ℝ*𝑠 ↾s ( 0 [,] +∞ ) ) = ( ℝ*𝑠 ↾s ( 0 [,] +∞ ) )
2		xrstopn	⊢ ( ordTop ‘ ≤ ) = ( TopOpen ‘ ℝ*𝑠 )
3	1 2	resstopn	⊢ ( ( ordTop ‘ ≤ ) ↾t ( 0 [,] +∞ ) ) = ( TopOpen ‘ ( ℝ*𝑠 ↾s ( 0 [,] +∞ ) ) )
4	3	eqcomi	⊢ ( TopOpen ‘ ( ℝ*𝑠 ↾s ( 0 [,] +∞ ) ) ) = ( ( ordTop ‘ ≤ ) ↾t ( 0 [,] +∞ ) )