In [8, 6] we introduced a family of ‘modal’ languages intended for talking about distances. These languages are interpreted in ‘distance spaces’ which satisfy some (or all) of the standard axioms of metric spaces. Among other things, we singled out decidable logics of distance spaces and proved expressive completeness results relating classical and modal languages. The aim of this paper is to a...

We study the complexity of expressing the greatest common divisor of n positive numbers as a linear combination of the numbers. We prove the NP-completeness of finding an optimal set of multipliers with respect to either the L0 metric or the L∞ norm. We present and analyze a new method for expressing the gcd of n numbers as their linear combination and give an upper bound on the size of the lar...

We present a general fixed point theorem which can be seen as the quintessence of the principles of proof for Banach’s Fixed Point Theorem and ultrametric fixed point theorems. It works in a minimal setting, not involving any metrics, only based on the notion of “ball” and the property of “spherical completeness”. We demonstrate its applications to the metric and the ultrametric cases, and (in ...

The paper is concerned with a very general version of Caristi’s coincidence theorem, in topological spaces (X, τ) satisfying some completeness conditions with respect to a function p : X ×X → [0,∞), and having as consequence Caristi’s fixed point theorem. The general result is applied to various concrete situations quasi-metric spaces, bornological spaces to obtain versions of Ekeland’s variati...

We introduce and study the framework of compact metric structures and their associated notions of isomorphisms such as homeomorphic and bi-Lipschitz isomorphism. This is subsequently applied to model various classification problems in analysis such as isomorphism of C∗-algebras and affine homeomorphism of Choquet simplices, where among other things we provide a simple proof of the completeness ...

Let L be an Archimedean Riesz space with a weak order unit u. A sufficient condition under which Dedekind [σ-]completeness of the principal ideal Au can be lifted to L is given (Lemma). This yields a concise proof of two theorems of Luxemburg and Zaanen concerning projection properties of C(X)-spaces. Similar results are obtained for the Riesz spaces Bn(T ), n = 1, 2, . . . , of all functions o...

*Correspondence: [email protected] Accounting School, Zhejiang University of Finance and Economics, Hangzhou, 310018, China Abstract By using R-weak commutativity of type (Ag) and non-compatible conditions of self-mapping pairs in generalized metric space, without the conditions for the completeness of space and the continuity of mappings, we establish some new common fixed point theorems for t...

The intent of this paper is to extend the notions of occasionally weakly compatible mappings, subcompatibility and subsequential continuity in framework of generalized metric spaces and prove some common fixed point theorems. We give some examples which demonstrate the validity of the hypotheses and degree of generality of our results. Our results are independent of the continuity requirement o...

According to the Einstein hole argument, vacuum metric solutions are equivalent only if they correspond same energy--momentum tensor in source region. In this paper it is shown that singular coordinates used show Schwarzschild geodesics completeness, introduce fictive delta-like sources at horizon. Then, tensors obtained by such transformations, cannot be considered as of equations with central...