The signature of the Poincaré duality of compact topological manifolds with local system of coefficients can be described as a natural invariant of nondegenerate symmetric quadratic forms defined on a category of infinite dimensional linear spaces. The objects of this category are linear spaces of the form W = V ⊕ V ∗ where V is abstarct linear space with countable base. The space W is consider...

Let (Xn)n∈ω be a sequence of uniform spaces such that each space Xn is a closed subspace in Xn+1. We give an explicit description of the topology and uniformity of the direct limit u-lim −→ Xn of the sequence (Xn) in the category of uniform spaces. This description implies that a function f : u-lim −→ Xn → Y to a uniform space Y is continuous if for every n ∈ N the restriction f |Xn is continuo...

VECTORIAL SEMANTICS AND SYNTAX OF LINEAR LOGICWith finiteness spaces, Ehrhard has shown a semantics of linear logic with a differentiationoperation. In this framework, the interpretation of formulas can be represented as Taylor series.This has led to the introduction of a differential syntax. This thesis in denotational semanticspursues this work through an exploration of ve...

For a symmetric monoidal-closed category X and any object K, the category of K-Chu spaces is small-topological over X and small cotopological over X . Its full subcategory of M-extensive K-Chu spaces is topological over X when X is Mcomplete, for any morphism class M. Often this subcategory may be presented as a full coreflective subcategory of Diers’ category of affine K-spaces. Hence, in addi...

M.Radulescu proved the following result: Let X be a compact Hausdorff topological space and π : C(X)→ C(X) a supra-additive and supra-multiplicative operator. Then π is linear and multiplicative. We generalize this result to arbitrary topological spaces.

let g = (v,e) be a locally finite graph, i.e. a graph in which every vertex has finitely many adjacent vertices. in this paper, we associate a topology to g, called graphic topology of g and we show that it is an alexandroff topology, i.e. a topology in which intersec- tion of every family of open sets is open. then we investigate some properties of this topology. our motivation is to give an e...

In this paper, we present a new vision for studying ${F}$-open, ${F}$-continuous, and ${F}$-irresolute function in $(L,M)$-fuzzy topological spaces based on the implication operation and $(L,M)$-fuzzy ${F}$-open operator cite{2}. These kinds of functions are generalized with their elementary properties to $(L,M)$-fuzzy topological spaces setting based on graded concepts. Moreover, a systematic ...

For non-metrizable spaces the classical Hausdorff dimension is meaningless. We extend the notion of Hausdorff dimension to arbitrary locally convex linear topological spaces, and thus to a large class of non-metrizable spaces. This involves a limiting procedure using the canonical bornological structure. In the case of normed spaces the new notion of Hausdorff dimension is equivalent to the cla...