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added hypotheses and top-level tag
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YCor
YCor
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If Y isLet $X$ be a topological space and $Y$ a topological group,. Then $C(X,Y)$ is C(Xa group,Y) and can also be endowed with the compact-open topology.

Is $C(X,Y)$ in the compact-open topology necessarily a topological group? If not, is there some property of X$X$ which will guarantee it?

If Y is a topological group, is C(X,Y) in the compact-open topology necessarily a topological group? If not, is there some property of X which will guarantee it?

Let $X$ be a topological space and $Y$ a topological group. Then $C(X,Y)$ is a group, and can also be endowed with the compact-open topology.

Is $C(X,Y)$ in the compact-open topology necessarily a topological group? If not, is there some property of $X$ which will guarantee it?

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Eli Falk
Eli Falk
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Does the compact-open topology retain topological groups?

If Y is a topological group, is C(X,Y) in the compact-open topology necessarily a topological group? If not, is there some property of X which will guarantee it?