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Central limit theorem for the average closure coefficient
Many real-world networks exhibit the phenomenon of edge clustering,which is typically measured by the average clustering coefficient. Recently,an...
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Convolution-Root Closure
Besides the convolution closure, it is often of interest to understand whether the attribution of a distribution F to the specific class of...
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On ring extensions pinched at the integral closure
The notion of the unique maximal overring of an integral domain is introduced and the domains for which the integral closure is the unique maximal...
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Homotopy, homology, and persistent homology using closure spaces
We develop persistent homology in the setting of filtrations of (Čech) closure spaces. Examples of filtrations of closure spaces include metric...
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Efficient realizations of closure systems
As is well-known, the subalgebras of any universal algebra form an algebraic closure system. Conversely, every algebraic closure system arises as the...
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Pachner’s Theorem
Pachner’s Theorem is a purely combinatorial theorem which plays an important role in low-dimensional topology. We give a topology-free self-contained...
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The Krein–Milman Theorem for Homogeneous Polynomials
This note addresses the problem of recovering a convex set of homogeneous polynomials from the subset of its extreme points, i.e., the justification...
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Tight Closure, Coherence, and Localization at Single Elements
In this note, a condition ( open persistence ) is presented under which a (pre)closure operation on submodules (resp. ideals) over rings of global...
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A decomposition theorem for unitary group representations on Kaplansky–Hilbert modules and the Furstenberg–Zimmer structure theorem
In this paper, a decomposition theorem for (covariant) unitary group representations on Kaplansky–Hilbert modules over Stone algebras is...
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Topology of closure systems in algebraic lattices
Algebraic lattices are spectral spaces for the coarse lower topology. Closure systems in algebraic lattices are studied as subspaces. Connections...
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The Whittaker Plancherel theorem
The purpose of this article is to give an exposition of a proof of the distributional form of the Whittaker Plancherel Theorem. The proof is an...
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The Diamond Theorem
Each finite proper separable extension of a Galois extension of a Hilbertian field K is Hilbertian. This is a theorem of Weissauer. Moreover, if L1...
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Polymatroids, Closure Operators and Lattices
In this article we study the closure operators of polymatroids from a lattice theoretic point of view. We show that polymatroid closure operators...
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Closure Lemmas for Interval Translation Map**s
AbstractInterval (circular arcs) translation map**s, which can be represented as interval exchange transformations with overlap, are studied. It is...
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Description of the Zariski-Closure of a Group of Formal Diffeomorphisms
Given a subgroup G of the group of germs of biholomorphisms, or more generally the group of formal diffeomorphisms, we provide a constructive...
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Regressive versions of Hindman’s theorem
When the Canonical Ramsey’s Theorem by Erdős and Rado is applied to regressive functions, one obtains the Regressive Ramsey’s Theorem by Kanamori and...
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Algebras of Binary Formulas for Weakly Circularly Minimal Theories with Trivial Definable Closure
We describe the algebras of binary formulas for countably categorical weakly circularly minimal theories with 1-transitive nonprimitive automorphism...
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A Metric Fixed Point Theorem and Some of Its Applications
A general fixed point theorem for isometries in terms of metric functionals is proved under the assumption of the existence of a conical bicombing....
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The s-Cobordism Theorem
In this chapter we want to discuss and prove the following theorem (in the smooth category).