1. $X$ is not a separable submetrizable, i.e.($iw(X)>\omega$) $X$ has not a countable injective weight.
  2. There is a Baire isomorphism 1-class between $X$ and a separable metrizable space $Y$.

Now take any uncountable $Q$-set $Y\subset R$ and let $X$ be the one-point compactification of a discrete space of cardinality $|Y|>\omega$.

| cite | improve this answer | |
  • $\begingroup$ Then $X$ and $Y$ is Borel isomorphic (1 - class), but $X$ and $Y$ is not Baire isomorphic ! So the question remains open ! $\endgroup$ – Alexander Osipov Nov 8 '17 at 6:33

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.