topological space

Is The Real Line Hausdorff?

by

Is The Real Line Hausdorff? Hausdorff space, in mathematics, type of topological space named for the German mathematician Felix Hausdorff. … Thus, the real line also becomes a Hausdorff space since two distinct points p and q, separated a positive distance r, lie in the disjoint open intervals of radius r/2 centred at p and

Is Every Locally Compact Space Is Compact?

by

Is Every Locally Compact Space Is Compact? Note that every compact space is locally compact, since the whole space X satisfies the necessary condition. Also, note that locally compact is a topological property. However, locally compact does not imply compact, because the real line is locally compact, but not compact. Is every open subspace of