Totally disconnected space
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LOCALLY NORMAL SUBGROUPS OF TOTALLY DISCONNECTED GROUPS. PART II: COMPACTLY GENERATED SIMPLE GROUPS Open
We use the structure lattice, introduced in Part I, to undertake a systematic study of the class $\mathscr{S}$ consisting of compactly generated, topologically simple, totally disconnected locally compact groups that are nondiscrete. Given…
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A product for permutation groups and topological groups Open
We introduce a new product for permutation groups. It takes as input two permutation groups, M and N, and produces an infinite group M [X] N which carries many of the permutational properties of M. Under mild conditions on M and N the grou…
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Free paratopological groups Open
Let FP(X) be the free paratopological group on a topological space X in the sense of Markov. In this paper, we study the group FP(X) on a $P_\alpha$-space $X$ where $\alpha$ is an infinite cardinal and then we prove that the group FP(X) is…
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The principal series of p‐adic groups with disconnected center Open
Let G be a split connected reductive group over a local non-Archimedean field. We classify all irreducible complex G-representations in the principal series, irrespective of the (dis)connectedness of the center of G. This leads to a local …
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About disconnected topologies and synchronization of homogeneous nonlinear agents over switching networks Open
Summary In this paper, we study the problem of networks on nonlinear oscillators when communication topologies are disconnected. In the first part of this paper, we show that the high‐gain design procedure succeeds in achieving clustered c…
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When God is your only friend: Religious beliefs compensate for purpose in life in the socially disconnected Open
Social relationships supply purpose to life. How can socially disconnected people, who show lower levels of purpose, compensate for purpose in life? We propose that religious beliefs can compensate for the purpose in life that social relat…
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A note on the interval function of a disconnected graph Open
In this note we extend the Mulder-Nebeský characterization of the interval function of a connected graph to the disconnected case. One axiom needs to be adapted, but also a new axiom is needed in addition.
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Topological and almost Borel Universality for systems with the weak\n specification property Open
We show that systems with some specification properties are topologically or\nalmost Borel universal, in the sense that any aperiodic subshift with lower\nentropy may be topologically or almost Borel embedded.\n
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Independent resolutions for totally disconnected dynamical systems. II. $C^*$-algebraic case Open
We develop the notion of independent resolutions for crossed products attached to totally disconnected dynamical systems. If such a crossed product admits an independent resolution of finite length, then its K-theory can be computed (at le…
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Homomorphisms into totally disconnected, locally compact groups with dense image Open
Let ϕ : G → H {\phi:G\rightarrow H} be a group homomorphism such that H is a totally disconnected locally compact (t.d.l.c.) group and the image of ϕ is dense. We show that all such homomorphisms arise as completions of G with respec…
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Topological entropy for locally linearly compact vector spaces Open
By analogy with the topological entropy for continuous endomorphisms of totally disconnected locally compact groups, we introduce a notion of topological entropy for continuous endomorphisms of locally linearly compact vector spaces. We st…
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On rectifiable measures in Carnot groups: Marstrand–Mattila rectifiability criterion Open
In this paper we continue the study of the notion of P-rectifiability in Carnot groups. We say that a Radon measure is Ph-rectifiable, for h∈N, if it has positive h-lower density and finite h-upper density almost everywhere, and, at almost…
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Separation, connectedness, and disconnectedness Open
The aim of this paper is to introduce the notions of hereditarily disconnected and totally disconnected objects in a topological category and examine the relationship as well as interrelationships between them. Moreover, we characterize ea…
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On Locating Chromatic Number of Disconnected Graph Open
Let is H a disconnected graph and c is the locating k -coloring of H . The locating-chromatic number of H , denoted by X L ' ( H ), is the smallest k such that H admits a locating-coloring with k colors. In this paper, we study the locatin…
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Homology and $K$-theory of dynamical systems II. Smale spaces with totally disconnected transversal Open
We apply our previous work on the relation between groupoid homology and K -theory to Smale spaces. More precisely, we consider the unstable equivalence relation of a Smale space with totally disconnected stable sets and prove that the ass…
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On full groups of non-ergodic probability-measure-preserving equivalence relations Open
This article generalizes our previous results [Le Maître. The number of topological generators for full groups of ergodic equivalence relations. Invent. Math. 198 (2014), 261–268] to the non-ergodic case by giving a formula relating the to…
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A Distinguished Subgroup of Compact Abelian Groups Open
Here “group” means additive abelian group. A compact group G contains δ–subgroups, that is, compact totally disconnected subgroups Δ such that G/Δ is a torus. The canonical subgroup Δ(G) of G that is the sum of all δ–subgroups of G turns o…
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Counting the Number of Disconnected Labeled Graphs of Order Five without Paralel Edges Open
— Given a graph G(V,E) with n vertices and m edges, where every vertex is labeled, there are a lot of possible graphs that can be constructed, either connected graphs or disconnected, simple or not simple. A graph G(V,E) is called as a con…
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Topological exodromy with coefficients Open
We improve the exodromy equivalence of MacPherson, Treumann and Lurie in several ways: first, we allow stratified spaces that have locally weakly contractible strata, rather than being locally of singular shape, we remove all noetherianity…
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Disconnected stationary solutions for 2D Kolmogorov flow problem in periodic domain Open
The classical A.N. Kolmogorov’s flow problem for the stationary 2D Navier-Stokes equations on a stretched torus for velocity vector function is considered. The problem is analysed by the construction of the solution curves in the parameter…
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Dynamics of flat actions on totally disconnected, locally compact groups Open
Let $G$ be a totally disconnected, locally compact group and let $H$ be a virtually flat (for example, polycyclic) group of automorphisms of $G$. We study the structure of, and relationships between, various subgroups of $G$ defined by the…
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Eremenko's conjecture, wandering Lakes of Wada, and maverick points Open
We develop a general technique for realising full closed subsets of the complex plane as wandering sets of entire functions. Using this construction, we solve a number of open problems. (1) We construct a counterexample to Eremenko's conje…
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Representation Theory of Disconnected Reductive Groups Open
We study three fundamental topics in the representation theory of disconnected algebraic groups whose identity component is reductive: (i) the classification of irreducible representations; (ii) the existence and properties of Weyl and dua…
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Distal actions on coset spaces in totally disconnected locally compact groups Open
Let [Formula: see text] be a totally disconnected locally compact (t.d.l.c.) group and let [Formula: see text] be an equicontinuously (for example, compactly) generated group of automorphisms of [Formula: see text]. We show that every dist…
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Homology and K-theory of dynamical systems III. Beyond stably disconnected Smale spaces Open
We study homological invariants of étale groupoids arising from Smale spaces, continuing on our previous work, but going beyond the stably disconnected case by incorporating resolutions in the space direction. We show that the homology gro…
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Even Harmonious Labelings of Disconnected Graphs Open
University of Minnesota M.S. thesis. May 2015. Major: Applied and Computational Mathematics. Advisor: Joseph Gallian. 1 computer file (PDF); v, 72 pages.
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Lipschitz invariance of walk dimension on connected self-similar sets Open
Walk dimension is an important conception in analysis of fractals. In this paper we prove that the walk dimension of a connected compact set possessing an Alfors regular measure is an invariant under Lipschitz transforms. As an application…
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Subgroups, hyperbolicity and cohomological dimension for totally disconnected locally compact groups Open
This paper is part of the program of studying large-scale geometric properties of totally disconnected locally compact groups, TDLC-groups, by analogy with the theory for discrete groups. We provide a characterization of hyperbolic TDLC-gr…
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Tree actions associated with the scale of an automorphism of a totally disconnected locally compact group Open
Research Doctorate - Doctor of Philosophy (PhD)%%%%One of the key features of the structure theory of totally disconnected locally compact groups is the existence of certain compact open subgroups, called tidy subgroups, which are well-beh…
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Disconnectedness properties of Hyperspaces Open
Let $X$ be a Hausdorff space and let $\mathcal{H}$ be one of the hyperspaces $CL(X)$, $\mathcal{K}(X)$, $\mathcal{F}(X)$ or $\mathcal{F}_n(X)$ ($n$ a positive integer) with the Vietoris topology. We study the following disconnectedness pro…