we show that the category of convergence approach spaces is a simultaneously reective and coreective subcategory of the category of latticevalued limit spaces. further we study the preservation of diagonal conditions, which characterize approach spaces. it is shown that the category of preapproach spaces is a simultaneously reective and coreective subcategory of the category of lattice-valued p...

A classical result of Toponogov [12] states that if a complete Riemannian manifold M with nonnegative sectional curvature contains a straight line, thenM is isometric to the metric product of a nonnegatively curved manifold and a line. We then know that the Busemann function associated with the straight line is an affine function, namely, a function which is affine on each unit speed geodesic i...

in this paper, we study some properties of the near sr-compactnessin l-topological spaces, where l is a fuzzy lattice. the near sr-compactness isa kind of compactness between lowen’s fuzzy compactness and sr-compactness,and it preserves desirable properties of compactness in general topologicalspaces.

Following the idea of $L$-fuzzy neighborhood system as introduced byFu-Gui Shi, and its generalization to $(L,M)$-fuzzy neighborhood system, the relationship between  $(L,M)$-fuzzy topology and $(L,M)$-fuzzy neighborhood system will be further studied. As an application of the obtained results, we will describe the initial structures of $(L,M)$-fuzzy neighborhood subspaces and $(L,M)$-fuzzy top...

In this paper we define an addition operation on the class of quasiconcave functions. While the new operation is similar to the well-known supconvolution, it has the property that it polarizes the Lebesgue integral. This allows us to define mixed integrals, which are the functional analogs of the classic mixed volumes. We extend various classic inequalities, such as the Brunn-Minkowski and the ...

Complete minimal surfaces and constant mean curvature surfaces in Euclidean or hyperbolic space have been the object of much attention in recent years and particular efforts have been devoted in understanding the moduli space of such surfaces. More precisely, the surfaces we are interested in are complete, noncompact surfaces which may or may not be embedded but enjoy the somehow weaker, and sl...

Melin, E. 2008. Digital Geometry and Khalimsky Spaces (Digital geometri och Khalimskyrum). Uppsala Dissertations in Mathematics 54. vii+47 pp. Uppsala. ISBN 978-91-506-1983-6 Digital geometry is the geometry of digital images. Compared to Euclid’s geometry, which has been studied for more than two thousand years, this field is very young. Efim Khalimsky’s topology on the integers, invented in t...

We prove the existence of Alexandrov embedded closed magnetic geodesics on any two dimensional sphere with nonnegative Gauß curvature.

Abstract In this article, we introduce a class of geometric optics measure-the L q Σ {L}_{q}\hspace{0.33em}\Sigma -reflector measure which arises from an {L}_{q} extension the \Sigma measure. And ask Minkows...