Dynamic Topological Logic (DT L) is a combination of S4, under its topological interpretation, and the temporal logic LT L interpreted over the natural numbers. DT L is used to reason about properties of dynamical systems based on topological spaces. Semantics are given by dynamic topological models, which are tuples 〈X, T , f, V 〉, where 〈X, T 〉 is a topological space, f a function on X and V ...

To any triangulated category with tensor product (K,⊗), we associate a topological space Spc(K,⊗), by means of thick subcategories of K, à la Hopkins-Neeman-Thomason. Moreover, to each open subset U of this space Spc(K,⊗), we associate a triangulated category K(U), producing what could be thought of as a presheaf of triangulated categories. Applying this to the derived category (K,⊗) := (D(X),⊗...

In [l] L. F. McAuley asked the following question: is it possible to partition . . . Moore's metrization theorem into three or more parts which begins with a condition for a topological space and which ends with a condition for a metrizable space, but with necessary and sufficient conditions somewhere between these extremes for semi-metric and Moore spaces? Axiom Z, stated below, is such a part...

Dynamic Topological Logic (DT L) is a combination of S4, under its topological interpretation, and the temporal logic LT L interpreted over the natural numbers. DT L is used to reason about properties of dynamical systems based on topological spaces. Semantics are given by dynamic topological models, which are tuples 〈X, T , f, V 〉, where 〈X, T 〉 is a topological space, f a function on X and V ...

Dynamic Topological Logic (DT L) is a modal logic which combines spatial and temporal modalities for reasoning about dynamic topological systems, which are pairs consisting of a topological space X and a continuous function f : X → X. The function f is seen as a change in one unit of time; within DT L one can model the long-term behavior of such systems as f is iterated. One class of dynamic to...

The purpose of this paper is to define the Fourier transform of an arbitrary tempered distribution on a reductive Lie group. To this end we define a topological vector space, [unk](G), in terms of the classes of irreducible unitary representations of G, which plays role of a dual Schwartz space. Our main theorem then asserts that the usual L(2) Fourier transform, when restricted to functions in...

A new definition of boundedness of linear order-homomorphisms (LOH)in $L$-topological vector spaces is proposed. The new definition iscompared with the previous one given by Fang [The continuity offuzzy linear order-homomorphism, J. Fuzzy Math. 5 (4) (1997)829$-$838]. In addition, the relationship between boundedness andcontinuity of LOHs is discussed. Finally, a new uniform boundednessprincipl...