Related papers: Modular Metric Spaces
We show, following W. Holsztynski, that there exists a continuous metric d on the set of real numbers R such that any finite metric space is isometrically embeddable into (R,d).
In this paper, we give an interesting extension of the partial S-metric space which was introduced [4] to the M_s-metric space. Also, we prove the existence and uniqueness of a fixed point for a self mapping on an Ms-metric space under…
Metric spaces are a fundamental component of mathematics and have a paramount importance as a framework for measuring distance. They can be found in many different branches of mathematics, such as analysis and topology. This paper offers an…
Recently Pelayo-V\~{u} Ngoc classified semitoric integrable systems in terms of five symplectic invariants. Using this classification we define a family of metrics on the space of semitoric integrable systems. The resulting metric space is…
Isaak Moiseevich Yaglom deduced complete classification of geometric spaces. In this work, supposed to your attention, author formalizes Yaglom's approach and constructs uniform theory of geometric spaces on analytic level. Among its…
We perform a detailed numerical investigation of the approximate moduli space metric proposed by Diakonov and Petrov [arXiv:0704.3181] for a confining model of dyons. Our findings strongly indicate that only for a small number of dyons at…
In the recent work [Metrically round and sleek metric spaces, \emph{The Journal of Analysis} (2022), pp 1--17], the authors proved some results on metrically round and sleek linear metric spaces and metric spaces. In continuation, the…
Thurston introduced in his seminal work an asymmetric metric on Teichm\"uller space by the ratio of simple closed curve length. In this paper, we generalize the idea and define an asymmetric metric on the space of unit-area flat metrics…
The paper aims to give an account, both historical and geometric, on the diverse geography of rational parametrizations of moduli spaces related to curves. It is a contribution to the book Handbook of Moduli, editors G. Farkas and I.…
In spacetime physics, we frequently need to consider a set of all spaces (`universes') as a whole. In particular, the concept of `closeness' between spaces is essential. However, there has been no established mathematical theory so far…
We introduced the concept of a metric value set (MVS) in an earlier paper \cite{GM} and developed the idea further in \cite{AS}. In this paper we study locally $M$-metrizable spaces and the products of $M$-metrizable spaces. Finally we…
This is a review article on mirror symmetry and aspects of it related to the theory of modular forms. We describe this topic along its historical development and connect to some more recent results toward the end. The article is for…
We survey recent work on moduli spaces of manifolds with an emphasis on the role played by (stable and unstable) homotopy theory. The theory is illustrated with several worked examples.
This paper has been withdrawn by the author due to a crucial error in the proofs. The error has been corrected and the paper has been expanded in arXiv:0910.5327
The main purpose of this manuscript is to provide a short proof of the metrizability of $\mathcal{F}$-metric spaces introduced by Jleli and Samet in \cite[\, Jleli, M. and Samet, B., On a new generalization of metric spaces, J. Fixed Point…
The moduli spaces refered to are topological spaces whose path components parametrize homotopy types. Such objects have been studied in two separate contexts: rational homotopy types, in the work of several authors in the late 1970's; and…
This paper is the first of three in which I study the moduli space of isometry classes of (compact) globally hyperbolic spacetimes (with boundary). I introduce a notion of Gromov-Hausdorff distance which makes this moduli space into a…
In this paper we correct an inaccuracy that appears in the proof of Theorem 1. in Czerwik's article "Contraction mappings in $b$-metric spaces.", Acta Math. Inform. Univ. Ostraviensis, 1:5--11, 1993.
This is an introduction to measure theory, integration and function spaces, with all the needed preliminaries included, and with some applications included as well. We first discuss some basic motivations, coming from discrete probability,…
In this paper, we give a approximation characterization, embedding properties and the duality of matrix weighted modulation spaces.