Let X be a Hausdorff topological space, Q(X, R) be the space of all quasicontinuous functions on X with values in R and τ UC be the topology of uniform convergence on compacta. If X is hemicompact, then (Q(X, R), τ UC) is metrizable and thus many cardinal invariants, including weight, density and cellularity coincide on (Q(X, R), τ UC). We find further conditions on X under which these cardinal invariants coincide on (Q(X, R), τ UC) as well as characterizations of some cardinal invariants of (Q(X, R), τ UC). It is known that the weight of continuous functions (C(R, R), τ UC) is ℵ 0. We will show that the weight of (Q(R, R), τ UC) is 2 c