A one-one selection theorem

Sarbadhikari, H.

doi:10.1090/S0002-9939-1986-0835890-4

A one-one selection theorem
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Proc. Amer. Math. Soc. 97 (1986), 320-322 Request permission

Abstract:

Let $X$, $Y$ be Polish spaces without isolated points and $B \subseteq X \times Y$ a Borel set such that $x:{B_x}$ is nonmeager is comeager in $X$ and $y:{B^y}$ is nonmeager is comeager in $Y$. There is a comeager Borel $E \subseteq X$, a comeager Borel $F \subseteq Y$ and a Borel isomorphism $f$ from $E$ onto $F$ such that graph of $f \subseteq B$.

References

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