The two-dimensional sphere can’t be approximated by finite homogeneous spaces. We describe the optimal approximation and its distance from sphere. compare this to achieved all Platonic Archimedean solids.

We prove that the only non-Archimedean strictly convex spaces are zero space and one-dimensional linear over $\, \mathbb{Z}/3\mathbb{Z}$, with any of its trivial norms.

An interesting question posed by Paul Erdös around 1950 pertains to the maximal number of points in n-dimensional Euclidean Space so that no subset of three points can be picked that form an obtuse angle. An unexpected and surprising solution was presented around a decade later. Interestingly enough the solution relies in its core on properties of measures in n-dimensional space. Beyond its int...

The aim of this paper is to introduce the concepts of compatible mappings and compatible mappings of type (R) in non-Archimedean Menger probabilistic normed spaces and to study the existence problems of common fixed points for compatible mappings of type (R), also, we give an applications by using the main theorems.