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...

Map Algebra is a collection of functions for handling continuous spatial data, which allows modeling of different problems and getting new information from the existing data. There is an established set of map algebra functions in the GIS literature, originally proposed by Dana Tomlin. However, the question whether his proposal is complete is still an open problem in GIScience. This paper descr...

We consider the topological entropy of state space and quasi-state space homeomorphisms induced from C∗-algebra automorphisms. Our main result asserts that, for automorphisms of separable exact C∗-algebras, zero Voiculescu-Brown entropy implies zero topological entropy on the quasi-state space (and also more generally on the entire unit ball of the dual). As an application we obtain a simple de...

The completion A[τ ] of a locally convex ∗-algebra A[τ ] with not jointly continuous multiplication is a ∗-vector space with partial multiplication xy defined only for x or y ∈ A0, and it is called a topological quasi ∗-algebra. In this paper two classes of topological quasi ∗-algebras called strict CQ-algebras and HCQ-algebras are studied. Roughly speaking, a strict CQ-algebra (resp. HCQ-algeb...

Two-dimensional topological field theories possessing a non-abelian current symmetry are constructed. The topological conformal algebra of these models is analysed. It differs from the one obtained by twisting the N = 2 superconfor-mal models and contains generators of dimensions 1, 2 and 3 that close a linear algebra. Our construction can be carried out with one and two bosonic currents and th...

Topological conformal field theories based on superconformal current algebras are constructed. The models thus obtained are the supersymmetric version of the G/G coset theories. Their topological conformal algebra is generated by operators of dimensions 1, 2 and 3 and can be regarded as an extension of the twisted N = 2 superconformal algebra. These models possess an extended supersymmetry whos...