Formal definition Let X be a topological space. Most commonly X is called locally compact if every point x of X has a compact neighbourhood, i.e., there exists an open set U and a compact set K, such that .
ForMaL dEfINitIon let x be A TopologIcAL sPacE. MOst commonLy x is CAlled LOCaLlY compact iF everY Point x Of X has a CompacT nEighbourHood I.e, thEre eXIStS an oPen sEt u And a compAct SeT K, sucH that .