in this paper, countable compactness and the lindel¨of propertyare defined for l-fuzzy sets, where l is a complete de morgan algebra. theydon’t rely on the structure of the basis lattice l and no distributivity is requiredin l. a fuzzy compact l-set is countably compact and has the lindel¨ofproperty. an l-set having the lindel¨of property is countably compact if andonly if it is fuzzy compact. ...

Graph comparison is a certain type of condition on the metric space encoded by finite graph. We show that each nontrivial graph implies one Alexandrov’s comparisons. The proof gives complete description graphs with trivial

the main purpose of this paper is to introduce a concept of$l$-fuzzifying topological groups (here $l$ is a completelydistributive lattice) and discuss some of their basic properties andthe structures. we prove that its corresponding $l$-fuzzifyingneighborhood structure is translation invariant. a characterizationof such topological groups in terms of the corresponding$l$-fuzzifying neighborhoo...

in 1997, fang proposed the concept of boundedness of $l$-fuzzy setsin $l$-topological vector spaces. since then, this concept has beenwidely accepted and adopted in the literature. in this paper,several characterizations of bounded $l$-fuzzy sets in$l$-topological vector spaces are obtained and some properties ofbounded $l$-fuzzy sets are investigated.

1. Demsar,I,2,3 V. V. Kabanov,I,3 A: S. Alexandrov,4 H. 1. Lee,5 E. D. Bauer,5 1. L. Sarrao,5 and A. 1. Taylor5 Iphysics Department and Zukunftskolleg, University of Konstanz, D-78457 Konstanz, Germany 2Center for Applied Photonics, University of Konstanz, D-78457 Konstanz, Germany 3Complex Matter Department, lozef Stefan Institute, SI-lOOO Ljubljana, Slovenia 4Department of Physics, Loughborou...

Grigory Perelman has been awarded the Fields Medal for his contributions to geometry and his revolutionary insights into the analytical and geometric structure of the Ricci flow. Perelman was born in 1966 and received his doctorate from St. Petersburg State University. He quickly became renowned for his work in Riemannian geometry and Alexandrov geometry, the latter being a form of Riemannian g...

This paper concerns the Riemannian/Alexandrov geometry of Gaussian measures, from the view point of the L2-Wasserstein geometry. The space of Gaussian measures is of finite dimension, which allows to write down the explicit Riemannian metric which in turn induces the L2-Wasserstein distance. Moreover, its completion as a metric space provides a complete picture of the singular behavior of the L...

in this paper, we investigate the l-fuzzy proximities and the relationships betweenl-fuzzy topologies, l-fuzzy topogenous order and l-fuzzy uniformity. first, we show that the category of-fuzzy topological spaces can be embedded in the category of l-fuzzy quasi-proximity spaces as a coreective full subcategory. second, we show that the category of l -fuzzy proximity spaces is isomorphic to the ...

in this paper, the urysohn and completely hausdorff axioms in general topology are generalized to l-topological spaces so as to be compatible with pointwise metrics. some properties and characterizations are also derived