Here we present an overview of countably-normed spaces. We discuss the main topologies—weak, strong, and inductive—placed on the dual of a countably-normed space and discuss the σ–fields generated by these topologies. In particular, we show that under certain conditions the strong and inductive topologies coincide and the σ–fields generated by the weak, strong, and inductive topologies are equa...

Themain purpose of this paper is to introduce a new structure that is a fuzzy TL-uniform space.We show that our structure generates a fuzzy topological space, precisely, a fuzzy Tlocality space. Also, we deduce the concept of level uniformities of a fuzzy TL-uniformity. We connect the category of fuzzy TL-uniform spaces with the category of uniform spaces. We establish a necessary and sufficien...

Here we present an overview of countably-normed spaces. We discuss the main topologies—weak, strong, and inductive—placed on the dual of a countably-normed space and discuss the σ–fields generated by these topologies. In particular, we show that under certain conditions the strong and inductive topologies coincide and the σ–fields generated by the weak, strong, and inductive topologies are equa...

We present a category of locally convex topological vector spaces which is a model of propositional classical linear logic, based on the standard concept of Köthe sequence spaces. In this setting, the “of course” connective of linear logic has a quite simple structure of commutative Hopf algebra. The co-Kleisli category of this linear category is a cartesian closed category of entire mappings. ...

We study topological D-branes of type B in N = 2 Landau-Ginzburg models, focusing on the case where all vacua have a mass gap. In general, tree-level topological string theory in the presence of topological D-branes is described mathematically in terms of a triangulated category. For example, it has been argued that B-branes for an N = 2 sigma-model with a CalabiYau target space are described b...

We study topological D-branes of type B in N = 2 Landau-Ginzburg models, focusing on the case where all vacua have a mass gap. In general, tree-level topological string theory in the presence of topological D-branes is described mathematically in terms of a triangulated category. For example, it has been argued that B-branes for an N = 2 sigma-model with a CalabiYau target space are described b...

We construct a classification of coherent sheaves with an integrable log connection, or, more precisely, sheaves with an integrable connection on a smooth log analytic space X over C. We do this in three contexts: sheaves and connections which are equivariant with respect to a torus action, germs of holomorphic connections, and finally global log analytic spaces. In each case, we construct an e...

in this paper, we first introduce some function spaces, with certain locally convex topologies, closely  related to the space of real-valued continuous functions on $x$,  where $x$ is a $c$-distinguished topological space. then, we show that their dual spaces can be identified in a natural way with certain spaces of radon measures.