We develop the flow analog of the classical Yosida adjunction between spaces and archimedean lattice-ordered groups with strong unit. A product of this development is the flow counterpart of the classical compactification of a space. We characterize those flows which are compactifiable, i.e., dense subflows of a compact flow. Finally, we exhibit a duality between the compactifications of a give...

This paper provides an overview of the theory of Bruhat-Tits buildings. Besides, we explain how Bruhat-Tits buildings can be realized inside Berkovich spaces. In this way, Berkovich analytic geometry can be used to compactify buildings. We discuss in detail the example of the special linear group. Moreover, we give an intrinsic description of Bruhat-Tits buildings in the framework of non-Archim...

Very recently, Proinov introduced a great family of contractions in the setting complete metric spaces that has attracted attention many researchers because very weak conditions are assumed on involved functions. Inspired by Proinov’s results, this paper, we introduce new class fuzzy (in sense George and Veeramani) able to translate framework best advantages abovementioned auxiliary Accordingly...

This article has three major goals. First, we define tropical cycle class maps for smooth varieties over non-Archimedean fields, valued in the Dolbeault cohomology defined in terms of real forms introduced by Chambert-Loir and Ducros. Second, we construct a functorial decomposition of de Rham cohomology sheaves, called weight decomposition, for smooth analytic spaces over certain non-Archimedea...

We prove a generic smoothness result in rigid analytic geometry over characteristic zero non-archimedean field. The proof relies on novel notion of points which are well adapted to ‘spreading out’ arguments, analogy with the use scheme theory. As an application, we develop six-functor formalism for Zariski-constructible étale sheaves spaces. Among other things, this implies that spaces support ...

After the definition of the concept of fuzzy metric space by some authors 1–3 , the fixed point theory on these spaces has been developing see, e.g., 4–9 . Generally, this theory on fuzzy metric space is done for contractive or contractive-type mappings see 2, 10–13 and references therein . In this paper we introduce the concept of fuzzy order ψ-contractive mappings and give two fixed point the...

For arbitrary real closed fields R, we study the structure of the space M(R(y)) of R-places of the rational function field in one variable over R and determine its dimension to be 1. We determine small subbases for their topology and discuss a suitable metric in the metrizable case. In the case of non-archimedean R, we exhibit the rich variety of homeomorphisms of subspaces that can be found in...

We prove generalized Hyres-Ulam-Rassias stability of the cubic functional equation f(kx + y) + f(kx − y) = k[f(x + y) + f(x − y)] + 2(k − k)f(x) for all k ∈ N and the quartic functional equation f(kx + y) + f(kx − y) = k[f(x + y) + f(x − y)] + 2k(k − 1)f(x)− 2(k − 1)f(y) for all k ∈ N in non-Archimedean normed spaces.

In this paper, we introduce the notion of fuzzy R−ψ−contractive mappings and prove some relevant results on existence uniqueness fixed points for type in setting non-Archimedean metric spaces. Several illustrative examples are also given to support our newly proven results. Furthermore, apply main a solution Caputo fractional differential equations.

Given a reductive group over complete non-Archimedean field, it is well known that techniques from analytic geometry provide an embedding of the corresponding Bruhat–Tits building into space associated with group; by composing maps to suitable proper spaces, this eventually leads various compactifications building. In present paper, we give intrinsic characterization embedding.