in this paper, using pre-semi-open l-sets and their inequality, a new notion of ps-compactness is introduced in l-topological spaces, where l is a complete de morgan algebra. this notion does not depend on the structure of the basis lattice l and l does not need any distributivity.

This paper gathers together some applications of quasigeodesic and gradient curves. After a discussion of extremal subsets, we give a proof of the Gluing Theorem for multidimensional Alexandrov spaces, and a proof of the Radius Sphere Theorem. This paper can be considered as a continuation of [Perelman and Petrunin 1994]. It gathers together some applications of quasigeodesic and gradient curve...

We summarize the results on the differential geometric structure of Alexandrov spaces developed in [Otsu and Shioya 1994; Otsu 1995; Otsu and Tanoue a]. We discuss Riemannian and second differentiable structure and Jacobi fields on Alexandrov spaces of curvature bounded below or above.

We present a substantial upgrade of our previously developed multi-filter rotating shadowband (MFRSR) data analysis algorithm (Alexandrov et al. 2002). For the new version an automated cloud screening procedure (Alexandrov et al. 2004) has been designed and a bimodal aerosol particle size distribution model is used defined by a variable fine mode size and a ratio between the fine and coarse modes.

Since Gromov gave in [G1], [G2] an abstract definition of Hausdorff distance between two compact metric spaces, the Gromov-Hausdorff convergence theory has played an important role in Riemannian geometry. Usually, Gromov-Hausdorff limits of Riemannian manifolds are almost never Riemannian manifolds. This motivates the study of Alexandrov spaces which are more singular than Riemannian manifolds ...

The aim of this paper is to extend the truth value table oflattice-valued convergence spaces to a more general case andthen to use it to introduce and study the quantale-valued fuzzy Scotttopology in fuzzy domain theory. Let $(L,*,varepsilon)$ be acommutative unital quantale and let $otimes$ be a binary operationon $L$ which is distributive over nonempty subsets. The quadruple$(L,*,otimes,varep...

In this paper we shall present a construction of Alexandrov-embedded complete surfaces M in R with nitely many ends and nite topology, and with nonzero constant mean curvature (CMC). This construction is parallel to the well-known original construction by Kapouleas [3], but we feel that ours somewhat simpler analytically, and controls the resulting geometry more closely. On the other hand, the ...

based on a complete heyting algebra l, the relations between lfuzzifyingconvergence spaces and l-fuzzifying topological spaces are studied.it is shown that, as a reflective subcategory, the category of l-fuzzifying topologicalspaces could be embedded in the category of l-fuzzifying convergencespaces and the latter is cartesian closed. also the specialization l-preorderof l-fuzzifying convergenc...

where xi are the coordinate functions on S". Minkowski then asked the converse of the problem. Namely, given a positive function K defined on S" satisfying the above integral conditions, can we find a closed strictly convex hypersurface whose curvature function is given by K? Minkowski solved the problem in the category of polyhedrons. Then A. D. Alexandrov and others solved the problem in gene...