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YCor
YCor
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Recently I read a book about linear algebraic group written by Ian Macdonald. There is a conclusion which I can't prove.

It says that if X$X$ is locally compact Hausdorff space, then X$X$ is compact if and only if, for all locally compact sapces Yspaces $Y$, the projection X$\times$Y $\to$ Y$X\times Y \to Y$ is a closed map. Is it a fact for all topology spaces?

Thank you in advance

Recently I read a book about linear algebraic group written by Ian Macdonald. There is a conclusion which I can't prove.

It says that if X is locally compact Hausdorff space, then X is compact if and only if, for all locally compact sapces Y, the projection X$\times$Y $\to$ Y is a closed map. Is it a fact for all topology spaces?

Thank you in advance

Recently I read a book about linear algebraic group written by Ian Macdonald. There is a conclusion which I can't prove.

It says that if $X$ is locally compact Hausdorff space, then $X$ is compact if and only if, for all locally compact spaces $Y$, the projection $X\times Y \to Y$ is a closed map. Is it a fact for all topology spaces?

Thank you in advance

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AGenevois
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A qustionquestion about locally compact spaces

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Fuutorider
Fuutorider
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A qustion about locally compact spaces

Recently I read a book about linear algebraic group written by Ian Macdonald. There is a conclusion which I can't prove.

It says that if X is locally compact Hausdorff space, then X is compact if and only if, for all locally compact sapces Y, the projection X$\times$Y $\to$ Y is a closed map. Is it a fact for all topology spaces?

Thank you in advance