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Each topological group embeds into a duoseparable topological group [PDF]
Topology Appl. 289 (2021) 107487, 2020 A topological group $X$ is called $duoseparable$ if there exists a countable set $S\subseteq X$ such that $SUS=X$ for any neighborhood $U\subseteq X$ of the unit. We construct a functor $F$ assigning to each (abelian) topological group $X$ a duoseparable (abelain-by-cyclic) topological group $FX$, containing an isomorphic copy of $X$.
T. Banakh, Igor Guran, A. Ravsky
arxiv +7 more sources
The fundamental group as a topological group [PDF]
Topology Appl. 160 (2013) 170-188, 2010 This paper is devoted to the study of a natural group topology on the fundamental group which remembers local properties of spaces forgotten by covering space theory and weak homotopy type. It is known that viewing the fundamental group as the quotient of the loop space often fails to result in a topological group; we use free topological groups to ...
Jeremy Brazas
arxiv +5 more sources
Topological Groups of Bounded Homomorphisms on a Topological Group [PDF]
Filomat, 2015 We consider a few types of bounded homomorphisms on a topological group. These classes of bounded homomorphisms are, in a sense, weaker than the class of continuous homomorphisms. We show that with appropriate topologies each class of these homomorphisms
L. Kočinac, O. Zabeti
semanticscholar +5 more sources
The topological fundamental group and free topological groups [PDF]
Topology Appl. 158 (2011) 779-802, 2010 The topological fundamental group $\pi_{1}^{top}$ is a homotopy invariant finer than the usual fundamental group. It assigns to each space a quasitopological group and is discrete on spaces which admit universal covers. For an arbitrary space $X$, we compute the topological fundamental group of the suspension space $\Sigma(X_+)$ and find that $\pi_{1}^{
arxiv +4 more sources
Topological Insulators from Group Cohomology [PDF]
Physical Review X, 2016 We classify insulators by generalized symmetries that combine space-time transformations with quasimomentum translations. Our group-cohomological classification generalizes the nonsymmorphic space groups, which extend point groups by real-space ...
A. Alexandradinata +2 more
doaj +2 more sources
On central topological groups [PDF]
Transactions of the American Mathematical Society, 1966 Grosser, Siegfried, Moskowitz, Martin
+6 more sources
Continuity in topological groups [PDF]
Proceedings of the American Mathematical Society, 1962 1. In the theory of topological groups, it is customary to make certain assumptions concerning the continuity of the product and continuity of the inverse. It has been noted that certain types of group spaces with less stringent assumptions than those usually made yield the ordinary assumptions [1; 2; 3; 4; 5].
Ta-Sun Wu
openaire +3 more sources
Topological Phases Protected by Point Group Symmetry [PDF]
Physical Review X, 2017 We consider symmetry-protected topological (SPT) phases with crystalline point group symmetry, dubbed point group SPT (pgSPT) phases. We show that such phases can be understood in terms of lower-dimensional topological phases with on-site symmetry and ...
Hao Song +3 more
doaj +2 more sources
Mathematica Moravica, 2021 In this paper, we introduce the notions of p-topological group and p-irresolute topological group which are generalizations of the notion topological group.
Jafari Saeid +2 more
doaj +1 more source
Progress and prospects in magnetic topological materials [PDF]
Nature, 2022 Magnetic topological materials represent a class of compounds with properties that are strongly influenced by the topology of their electronic wavefunctions coupled with the magnetic spin configuration.
B. Bernevig, C. Felser, H. Beidenkopf
semanticscholar +1 more source