In this paper, the gradual real numbers are considered and the notion of the gradual normed linear space is given. Also some topological properties of such spaces are studied, and it is shown that the gradual normed linear space is a locally convex space, in classical sense. So the results in locally convex spaces can be translated in gradual normed linear spaces. Finally, we give an examp...

This paper is a continuation of [8] and in it some applications of the methods and results of [8] and of [28, 7, 24, 9, 10, 11] are given. In particular, a slight generalization of the Stone’s results [28] concerning the extension of his Duality Theorem to the category of locally compact zerodimensional Hausdorff spaces is obtained; a completion theorem for local contact Boolean algebras is pro...

The notion of finitary spacetime sheaves is introduced based on locally finite approximations of the continuous topology of a bounded region of a spacetime manifold. Finitary spacetime sheaves are seen to be sound mathematical models of approximations of continuous spacetime observables.

We introduce the notion of tropical Lagrangian multi-sections over a $2$-dimensional integral affine manifold $B$ with singularities, and use them to study reconstruction problem for higher rank locally free sheaves Calabi-Yau surfaces. To certain $\mathbb{L}$ $B$, which are explicitly constructed by prescribing local models around ramification points, we construct $\mathcal{E}_0(\mathbb{L},{\b...

Admissible locally-free sheaves on P, also known in the literature as mathematical instanton bundles, arise in twistor theory, and are in 1-1 correspondence with instantons on R. In this paper, we study admissible sheaves on P from the algebraic geometric point of view. We discuss examples and compare the admissibility condition with semistability and splitting type.

Given a Polish group G of isometries of a locally compact separable metric space, we prove that each measure preserving Boolean action by G has a spatial model or, in other words, has a point realization. This result extends both a classical theorem of Mackey and a recent theorem of Glasner and Weiss, and it covers interesting new examples. In order to prove our result, we give a characterizati...