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 ...

In this paper, characterizations of the degree to which a mapping $mathcal{T} : L^{X}longrightarrow M$ is an $(L, M)$-fuzzy topology are studied in detail.What is more, the degree to which an $L$-subset is an $L$-open set with respect to $mathcal{T}$ is introduced.Based on that, the degrees to which a mapping $f: Xlongrightarrow Y$ is continuous,open, closed or a quotient mapping with respect t...

Since Chang [2] introduced fuzzy theory into topology, many authors have discussed various aspects of fuzzy topology. It is well known that weakly induced and induced topological spaces play an important role in L-topological spaces (see book [8]). According to their value ranges, L-topological spaces form different categories. Clearly, the investigation on their relationships is certainly impo...

The concepts of β-compactness and βclosed spaces in the fuzzy setting are defined and investigated. Fuzzy filterbases are used to characterize these concepts. A comparison between these types and some different forms of compactness in fuzzy topology is established.

We study the fuzzy soft proximity spaces in Katsaras's sense. First, we show how a fuzzy soft topology is derived from a fuzzy soft proximity. Also, we define the notion of fuzzy soft δ-neighborhood in the fuzzy soft proximity space which offers an alternative approach to the study of fuzzy soft proximity spaces. Later, we obtain the initial fuzzy soft proximity determined by a family of fuzzy ...

The notion of separatedness degrees of L-fuzzy subsets is introduced in L-fuzzy topological spaces by means of L-fuzzy closure operators. Furthermore, the notion of connectedness degrees of L-fuzzy subsets is introduced. Many properties of connectedness in general topology are generalized to L-fuzzy topological spaces.

In the present paper we introduce the topological structure of fuzzy soft sets and fuzzy soft continuity of fuzzy soft mappings. We show that a fuzzy soft topological space gives a parametrized family of fuzzy topological spaces. Furthermore, with the help of an example it is shown that the constant mapping is not continuous in general. Then the notions of fuzzy soft closure and interior are in...

It is shown that every fuzzy n-normed space naturally induces a locally convex topology, and that every finite dimensional fuzzy n-normed space is complete.