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## Main Question or Discussion Point

hi.. how can we say a compact space automatically a locally compact? how subspace Q of rational numbers is not locally compact? am not able to understand these.. can anyone help me?

- Thread starter winmath
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hi.. how can we say a compact space automatically a locally compact? how subspace Q of rational numbers is not locally compact? am not able to understand these.. can anyone help me?

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- #3

Landau

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Why do you say "in a certain sense"? It's just weaker; locally compact means: every point has a compact neighbourhood. If the whole space is compact, for any point you just take the whole space as compact neighborhood.Locally compact is in a certain sense a weaker assertion than compactness.

Just try to find a compact neighborhood of q\in Q.how subspace Q of rational numbers is not locally compact?

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