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Let X, Y $X, Y$ be two metric spaces and f $f$ be a continuous bijection (i.e. one-to-one map) from X $X$ to Y. $Y$. Let E $E$ be a G_\delta $G_{\delta}$ subset of X. $X$. I want to know weather the image f(E) $f(E)$ is also a G_\delta $G_{\delta}$ subset of Y. $Y$. Thanks!

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# On the image of a G_\delta set under a continuous bijection

Let X, Y be two metric spaces and f be a continuous bijection (i.e. one-to-one map) from X to Y. Let E be a G_\delta subset of X. I want to know weather the image f(E) is also a G_\delta subset of Y. Thanks!