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Ittay Weiss
Ittay Weiss
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Your tutor is wrong. Every homeomorphism (such as $\exp:\mathbb R\to\mathbb R_{>0}$) is closed. The standard topology on the codomainset $\mathbb R_{>0}$ is thea closed set of all open sets of $\mathbb R$ intersected with $\mathbb R_{>0}$, and in this topology, the setstandard topology on $\mathbb R_{>0}$ is a closed set.

Your tutor is wrong. Every homeomorphism (such as $\exp:\mathbb R\to\mathbb R_{>0}$ is closed. The standard topology on the codomain $\mathbb R_{>0}$ is the set of all open sets of $\mathbb R$ intersected with $\mathbb R_{>0}$, and in this topology, the set $\mathbb R_{>0}$ is a closed set.

Your tutor is wrong. Every homeomorphism (such as $\exp:\mathbb R\to\mathbb R_{>0}$) is closed. The set $\mathbb R_{>0}$ is a closed set in the standard topology on $\mathbb R_{>0}$.

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Samuel
Samuel
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Your tutor is wrong. Every homeomorphism (such as $\exp:\mathbb R\to\mathbb R_{>0}$ is closed. The standard topology on the codomain $\mathbb R_{>0}$ is the set of all open sets of $\mathbb R$ intersected with $\mathbb R_{>0}$, and in this topology, the set $\mathbb R_{>0}$ is a closed set.