Let X be a convex subset of a locally convex topological vector space, let U ⊂ X be open with U compact, let F : U → X be an upper semicontinuous convex valued correspondence with no fixed points in U \U , let P be a compact absolute neighborhood retract, and let ρ : U → P be a continuous function. We show that if the fixed point index of F is not zero, then there is a neighborhood V of F in th...

We present an axiomatic approach to finiteand infinite-dimensional differential calculus over arbitrary infinite fields (and, more generally, suitable rings). The corresponding basic theory of manifolds and Lie groups is developed. Special attention is paid to the case of mappings between topological vector spaces over non-discrete topological fields, in particular ultrametric fields or the fie...

For every filter F on N, we introduce and study corresponding uniform F-boundedness principles for locally convex topological vector spaces. These generalise the classical boundedness sequences of continuous linear maps by coinciding with these when equals Fréchet cofinite subsets N. We determine combinatorial properties which ensure that hold space. Furthermore, several types spaces, also isol...

In this work, we consider a generalized nonlinear variational-like inequality problem in the setting of locally convex topological vector spaces and prove the existence of its solutions. © 2005 Published by Elsevier Ltd MSC: 49J40; 47H19; 47H10

This paper discusses under what conditions two disjoint convex subsets of a linear topological space can be separated by a continuous linear functional. The equivalence of several forms of the Hahn-Banach theorem is proven. The separation problem is considered in linear topological spaces, locally convex linear topological spaces, Banach spaces, and finally finite dimensional Banach spaces. A n...

The first point here is that convex sets can be separated by linear functionals. Second, continuous linear functionals on subspaces of a locally convex topological vectorspace have continuous extensions to the whole space. Proofs are for real vectorspaces. The complex versions are corollaries. A crucial corollary is that on locally convex topological vectorspaces continuous linear functionals s...

A topological algebra is a complex associative algebra which is also a Hausdorff topological vector space such that the multiplication is separately continuous. A locally convex algebra is a topological algebra whose topology is determined by a family of seminorms. A complete metrizable locally convex algebra is called a B0-algebra. The topology of a B0-algebra A may be given by a countable fam...