Let $U$ be an open subset of $\mathbb{R}^n$, is there a continuous injective function $f$ from $U$ to $\mathbb{R}^n$ whose image is not open?
2026-04-07 22:45:18.1775601918
Are injective continuous functions on open sets open?
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The injective continuous image of an open $U\subseteq\mathbb{R}^n$ in $\mathbb{R}^n$ is always open - this is a consequence of invariance of domain.