Theorem xrge0topn

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

	Ref	Expression
Assertion	xrge0topn	|- ( TopOpen ` ( RR*s |`s ( 0 [,] +oo ) ) ) = ( ( ordTop ` <_ ) |`t ( 0 [,] +oo ) )

Proof

Step	Hyp	Ref	Expression
1		eqid	|- ( RR*s |`s ( 0 [,] +oo ) ) = ( RR*s |`s ( 0 [,] +oo ) )
2		xrstopn	|- ( ordTop ` <_ ) = ( TopOpen ` RR*s )
3	1 2	resstopn	|- ( ( ordTop ` <_ ) |`t ( 0 [,] +oo ) ) = ( TopOpen ` ( RR*s |`s ( 0 [,] +oo ) ) )
4	3	eqcomi	|- ( TopOpen ` ( RR*s |`s ( 0 [,] +oo ) ) ) = ( ( ordTop ` <_ ) |`t ( 0 [,] +oo ) )