Definition. Quasi locally compact space [mde-SI1D]

A topological space is quasi locally compact or core-compact if for every point \(x\) and open neighbourhood \(U\) of \(x\) there exists an open neighbourhood \(V\) of \(x\) such that any open cover of \(U\) has a finite subcover covering \(V\), denoted \(V \ll U\).

Quasi locally compact spaces are the exponentiable objects of \(\mathbf {Top}\).