Suppose \(X\) is Hausdorff and has a basis consisting of sets that are both open and closed. Show that \(X\) is totally disconnected; that is, every connected subset of \(X\) consists of one point.
A Hausdorff space with a clopen basis is totally disconnected
P-WESTOP11-7
- Area
- Topology
- Seen at
- WESLEYAN
- Years
- 2011
- Status
- draft