I'm studying my set theory lessons and I don't know if the following statement about homeomorphism between ordinal spaces is true or not and why.
"If $\kappa$ is an infinite cardinal number then $[0,\kappa]$ is not homemorphic to $[0,\kappa+\kappa]$"
If anyone could help me I would be grateful.
HINT: $[0,\kappa+\kappa]$ has two disjoint compact sets of cardinality $\kappa$; does $[0,\kappa]$?