Description: The topology of the extended reals is connected. (Contributed by Mario Carneiro, 9-Sep-2015)
Ref | Expression | ||
---|---|---|---|
Assertion | xrconn | |- ( ordTop ` <_ ) e. Conn |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | xrhmph | |- II ~= ( ordTop ` <_ ) |
|
2 | iiconn | |- II e. Conn |
|
3 | connhmph | |- ( II ~= ( ordTop ` <_ ) -> ( II e. Conn -> ( ordTop ` <_ ) e. Conn ) ) |
|
4 | 1 2 3 | mp2 | |- ( ordTop ` <_ ) e. Conn |