Minimal usco and minimal cusco maps and the topology of pointwise convergence

Abstract Let X be a Hausdorff topological space, MU ( X , ℝ) and MC ( X , ℝ) be the space of all minimal usco maps with values in ℝ and the space of all minimal cusco maps with values in ℝ, respectively. By τ p is denoted the topology of pointwise convergence. We characterize some cardinal invariants of ( MU ( X , ℝ) , τ p ) and ( MC (ℝ,ℝ) , τ p ). Let Q (ℝ,ℝ) be the space of all quasicontinuous functions on ℝ with values in ℝ and C (ℝ,ℝ) the space of all continuous functions on ℝ with values in ℝ. We compare cardinal invariants of ( MU (ℝ,ℝ) , τ p ), ( MC (ℝ,ℝ) , τ p ), ( Q (ℝ,ℝ) , τ p ) and ( C (ℝ,ℝ) , τ p ).