# Is there a Tychonoff space $X$ such that …?

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