Introducing certain types of morphisms for general (abstract) convexity spaces, we give several ways for reducing the (Calder-) Eckhoff partition problem to simpler equivalent forms (finite, point-convex, interval spaces; restricted form, i.e. with distinct points). With additional results (to appear in a forthcoming paper) we show how the general problem can be reduced to its restricted versio...

The main purpose of this paper is to study the weight under hereditarily irreducible mappings between continua. The main result states that if f : X → Y is an hereditarily irreducible and surjective mapping of a D-continuum X, then w(X) = w(Y ).

It is still a long-standing open problem in Finsler geometry, there any regular Landsberg metric which not Berwaldian. However, are non-regular metrics The known examples established by G. S. Asanov and Z. Shen. In this paper, we use the Maple program to study some explicit of non-Berwaldian metrics. fact, such kinds very tedious complicated investigate. Nonetheless, packages simplify calculati...

The authors use techniques and results from the theory of generalized metric spaces to give a new, short proof that every connected, linearly ordered topological space that is a cancellative topological semigroup is metrizable, and hence embeddable in R. They also prove that every separable, linearly ordered topological space that is a cancellative topological semigroup is metrizable, so embedd...

Ťhis note tries to give an answer to the following question: Is there a sufficiently rich class of metric vector spaces such that sufficiently large spaces of continuous linear maps between them are metrizable?

In this paper we show that by renorming an ordered Banach space, every cone P can be converted to a normal cone with constant K = 1 and consequently due to this approach every cone metric space is really a metric one and every theorem in metric space is valid for cone metric space automatically.