In the present paper we prove a unique common fixed point theorem for four weakly compatible self maps in non Archimedean Menger Probabilistic Metric spaces without using the notion of continuity. Our result generalizes and extends the results of Amit Singh, R.C. Dimri and Sandeep Bhatt [A common fixed point theorem for weakly compatible mappings in non-Archimedean Menger PM-space, MATEMATIQKI ...

We shall find the following necessary and sufficient conditions: I. the space is metrizable (cf. Nagata [l], Smirnof [2]), II. the space is strongly O-dimensional. Property II means that any two closed disjoint sets in the space can be separated (by the empty set). We shall prove furthermore that the conditions I and II are equivalent to the following topological properties: the space is a Haus...

We outline the classification of K-rank 1 groups over non-archimedean local fields K up to strict isogeny, as in [Ti1] and [Ti2]. We outline the classification of absolutely simple algebraic groups over non-archimedean local fields, up to strict isogeny. This is classical, and accounts of it have been written by Tits ([Ti1], [Ti2]) and Satake ([Sa]). Tits compiled tables of ‘admissible indices’...

We explore the distinction between convergence and absolute convergence of series in both Archimedean and non-Archimedean ordered fields and find that the relationship between them is closely connected to sequential (Cauchy) completeness.

A non-Archimedean analog of the classical Big Picard Theorem, which says that a holomorphic map from the punctured disc to a Riemann surface of hyperbolic type extends accross the puncture, is proven using Berkovich’s theory of non-Archimedean analytic spaces.

For more than two millennia, ever since Euclid’s geometry, the so called Archimedean Axiom has been accepted without sufficiently explicit awareness of that fact. The effect has been a severe restriction of our views of space-time, a restriction which above all affects Physics. Here it is argued that, ever since the invention of Calculus by Newton, we may actually have empirical evidence that t...