An object $X$ of a category $mathbf{C}$ with finite limits is called exponentiable if the functor $-times X:mathbf{C}rightarrow mathbf{C}$ has a right adjoint. There are many characterizations of the exponentiable  spaces in the category $mathbf{Top}$ of topological spaces. Here, we study the exponentiable objects in the category $mathbf{STop}$ of soft topological spaces which is a generalizati...

We study a family of subrings, indexed by the natural numbers, of the mod p cohomology of a finite group G. These subrings are based on a family of vn-periodic complex oriented cohomology theories and are constructed as rings of generalised characteristic classes. We identify the varieties associated to these subrings in terms of colimits over categories of elementary abelian subgroups of G, na...

It is well known that a microperiodic function mapping a topological group into reals, which is continuous at some point is constant. We introduce the notion of a microperiodic multifunction, defined on a topological group with values in a metric space, and study regularity conditions implying an analogous result. We deal with Vietoris and Hausdorff continuity concepts.Stability of microperiodi...

The aim of this paper is to show that every topological space gives rise to a wealth of topological models of the modal logic S4.1. The construction of these models is based on the fact that every topological space defines a Boolean closure algebra (to be called a McKinsey algebra) that neatly reflects the structure of the modal system S4.1 in that all its elements satisfy the topological inter...

This is the first of two papers in which we prove that a cell model of the moduli space of curves with marked points and tangent vectors at the marked points acts on the Hochschild co–chains of a Frobenius algebra. We also prove that a there is dg–PROP action of a version of Sullivan Chord diagrams which acts on the normalized Hochschild co-chains of a Frobenius algebra. These actions lift to o...