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?
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?