We are familar with that for the first uncountable cardinality $\omega_1$, the topological space $[0,\omega_1]$ is compact. I find the proof for the $\omega_1$, is also for every regular cardinality. So is there a result for every regular cardinality, i.e.,
For every regular cardinality $\kappa$ with order topology, then $\kappa\cup \{\kappa\}$ is compact?
Am I right? Thanks for any help:)