I learnt from a paper that "Let cov(K) be the least cardinal k such that a perfect Polish space can be expressed as a union of k meager sets. (It does not matter which perfect Polish space is used to define cov(K) ) " . I don't know why cov(K)'s are equal for different perfect Polish spaces. I want to use this result in my own paper, but I fail to find any books contain this result, could anybody kindly to help me ?



Covering number of the meager ideal
This should be in standard texts on descriptive set theory, like Moschovakis's "Descriptive Set Theory" or Kechris's "Classical Descriptive Set Theory". The basic idea is that any two perfect Polish spaces become homeomorphic after you remove (at most) countably many points. Countably many points constitute a meager set and therefore don't affect cov(K).


