Sequentailly Compact and Connected

[Paper Wings]

Homework Statement

Which subset of R are both sequentially compact and connected?

Homework Equations

The Attempt at a Solution

The connected subsets of R are the empty set, points, and intervals.
The subsets of R that are compact are closed and bounded.

Thus, the subsets of R that are both sequentially compact and connected are closed, bounded continuous intervals. Is this correct?

 

[Dick]

I'm convinced. But I don't think you need to say an interval is 'continuous'. If you mean 'without holes' isn't that automatic?

 

[Paper Wings]

Yes, I see what you mean. Thank you.

Does anyone know how to close or edit the words "SOLVED" in threads?