Some properties related to the Cantor-Bendixson derivative on a Polish space

We show a necessary and sufficient condition for any ordinal number to be Polish space. also prove that each countable space, there exists is an upper bound the first component of Cantor-Bendixson characteristic every compact subset aforementioned In addition, uncountable nonzero natural number, we existence this space such its equals previous pair numbers. Finally, determine cardinality partition, up homeomorphisms, set all subsets aforesaid