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.

Under new assumptions, we provide suffcient conditions for the upper and lower semicontinuity and continuity of the solution mappings to a class of generalized parametric set-valued Ky Fan inequality problems in linear metric space. These results extend and improve some known results in the literature e.g., Gong, 2008; Gong and Yoa, 2008; Chen and Gong, 2010; Li and Fang, 2010 . Some examples a...

We prove an incidence theorem for points and curves in the complex plane. Given a set of m points in R and a set of n curves with k degrees of freedom, Pach and Sharir proved that the number of point-curve incidences is O ( m k 2k−1n 2k−2 2k−1 +m+n ) . We establish the slightly weaker bound Oε ( m k 2k−1 n 2k−2 2k−1 +m+n ) on the number of incidences between m points and n (complex) algebraic c...

We use graph convergence of set valued maps to show the existence of an equilibrium for an abstract economy without assuming the lower semi continuity of the constraint maps.

We introduce the notion of a C *-valued weight between two C *-algebras as a generalization of an ordinary weight on a C *-algebra and as a C *-version of operator valued weights on von Neumann algebras. Also, some form of lower semi-continuity will be discussed together with an extension to the Multiplier algebra. A strong but useful condition for C *-valued weights, the so-called regularity, ...

In this paper, we introduce intuitionistic smooth bitopological spaces and the notions of intuitionistic fuzzy semiinterior and semiclosure. Based on these concepts, the characterizations for the intuitionistic fuzzy pairwise semicontinuous mappings are obtained.

An effectivity function assigns to each coalition of individuals in a society a family of subsets of alternatives such that the coalition can force the outcome of society’s choice to be a member of each of the subsets separately. A representation of an effectivity function is a game form with the same power structure as that specified by the effectivity function. In the present paper we investi...

We study incremental problems in geometrically nonlinear elastoplasticity. Using the multiplicative decomposition Dφ = FelFpl we consider general energy functionals of the form