We show that the space of all Lelek fans in a Cantor fan, equipped with the Hausdorff metric, is homeomorphic to the separable Hilbert space. This result is a special case of a general theorem we prove about spaces of upper semicontinuous functions on compact metric spaces that are strongly discontinuous.

In this paper we study the solvability of a system of vector equilibrium problems. We extend the concept of topological pseudomonotonicity to a family of mappings. We prove existence results for the system of vector equilibrium problems under topological pseudomonotonicity conditions by the Kakutani-Fan-Glicksberg fixed point theorem. As applications, we obtain existence results for systems of ...

In this thesis, we will discuss Freiling’s axiom of symmetry from an intuitionistic point of view. Using Brouwer’s Continuity Principle and fan theorem, we will find that the natural interpretation of this axiom holds in intuitionistic mathematics. The same is true for most of the extensions formulated by Freiling, in so far as they have a natural interpretation in intuitionism.

For a complete toric variety, we obtain an explicit formula for the localized equivariant Todd class in terms of the combinatorial data – the fan. This is based on the equivariant Riemann-Roch theorem and the computation of the equivariant cohomology and equivariant homology of toric varieties. ∗This research was supported in part by NSF grant DMS-9504522 and DMS-9803593

A torus orbifold is an oriented closed orbifold of even dimension which admits an action of a torus of half the dimension of the orbifold with some orientation data concerning codimension two fixed point set components of circle subgroups and with some restrictions on isotropy groups of points of the orbifold. Typical examples are complete toric varieties with simplicial fan. To a toric variety...