Related papers: On Scalable Monoids
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 based on a mini-course comprised of four talks given by the author at Berkeley.
In this article we survey, and make a few new observations about, the surprising connection between sub-monoids of mapping class groups and interesting geometry and topology in low-dimensions.
A didactic introduction, dated by 1999, to the ideas of the papers arXiv:q-bio/0701050 and arXiv:0704.0034
Within a subclass of monoids (with zero) a structural characterization is given of those that are associated to topologically transitive subshifts with Property (A).
These notes are an introduction to the theory of quantum symmetries of finite and infinite sets, graphs, and locally compact spaces.
These are some informal notes concerning topological vector spaces, with a brief overview of background material and basic notions, and emphasis on examples related to classical analysis.
The soft topological spaces and some their related concepts have stud- ied in [7]. In this paper, we introduce and study the notions of soft connected topological spaces after a review of preliminary definitions.
In this note we extend the concept height on projective spaces to that of weighted height on weighted projective spaces and show how such a height can be computed. We prove some of the basic properties of the weighted height and show how it…
In this article, we introduce the concept of lexicographic metric space and, after discussing some basic properties of these metric spaces, such as completeness, boundedness, compactness and separability, we obtain a formula for the metric…
This paper expands on and refines some known and less well-known results about the finite subset spaces of a simplicial complex $X$ including their connectivity and their top homology groups. It also discusses the inclusion of the…
This is the first part of a series of three strongly related papers in which three equivalent structures are studied: - internal categories in categories of monoids; defined in terms of pullbacks relative to a chosen class of spans -…
The article provides a brief general introduction into the concepts of scaling, universality, and crossover scaling, plus the blob concept that provides an intuitive picture of crossover phenomena. We present the most important static and…
In this paper the concept of a partial cone metric space is investigated, some continuity type theorems, and fixed point theorems of contractive mappings in this generalized setting are proved as well as some theorems related to topological…
The goal of this article was the S^1-equivariant transversality-problem and the compactification-problem for the moduli spaces of (perturbed) PU(2)-monopoles. A substantially improved version entitled "Moduli spaces of PU(2)-monopoles…
In this note we make a minor correction to the paper ``Simplicial monoids and Segal categories."
A general result relating skew monoidal structures and monads is proved. This is applied to quantum categories and bialgebroids. Ordinary categories are monads in the bicategory whose morphisms are spans between sets. Quantum categories…
We show that being finitely presentable and being finitely presentable with solvable word problem are quasi-isometry invariants of finitely generated left cancellative monoids. Our main tool is an elementary, but useful, geometric…
In this short note we present several infinite dimensional theorems which generalize corresponding facts from the finite dimensional differential inclusions theory.
These lectures give a short introduction to the study of curves on algebraic varieties. After an elementary proof of the dimension formula for the space of curves, we summarize the basic properties of uniruled and of rationally connected…