We extend some topologies on the space of upper semicontinuous functions with compact support to those on that of general upper semicontinuous functions and see that graphical topology and modified L topology are the same. We then define random upper semicontinuous functions using their topological Borel field and finally give a Choquet theorem for random upper semicontinuous functions.

Several classes of hereditarily normal spaces are characterized in terms of extending upper semi-continuous compact-valued mappings. The case of controlled extensions is considered as well. Applications are obtained for real-valued semi-continuous functions.

If U and V are topologies on an abstract set X, then the triple (X, U, V) is a bitopological space. Using the theorem of Priestley on the representation of distributive lattices, results of Dilworth concerning the normal completion of the lattice of bounded, continuous, realvalued functions on a topological space are extended to include the lattice of bounded, semi-continuous, real-valued funct...

Assume that X is a metrizable separable space, and each clopen-valued lower semicontinuous multivalued map Φ : X ⇒ Q has a continuous selection φ : X → Q. Our main result is that in this case, X is a σ-space. We also derive a partial converse implication, and present a reformulation of the Scheepers Conjecture in the language of continuous selections.

This study analyses the concept of cost functions for semi-automated Straddle Carrier (SC), Rubber Tyred Gantry (RTG) and automated Rail Mounted Gantry (RMG) container yard operating cranes. It develops a generic cost based model for a pair-wise comparison, analysis and evaluation of economic efficiency and effectiveness of container yard equipment to be used for decision-making by terminal pla...