Topological group
View article
Geometric Group Theory Open
The primary focus of this book is to cover the foundations of geometric group theory, including coarse topology, ultralimits and asymptotic cones, hyperbolic groups, isoperimetric inequalities, growth of groups, amenability, Kazhdan's ...
View article
Topological correspondence between magnetic space group representations and subdimensions Open
The past years have seen rapid progress in the classification of topological\nmaterials. These diagnostical methods are increasingly getting explored in the\npertinent context of magnetic structures. We report on a general class of\nelectr…
View article
Weak group inverse Open
In this paper, we introduce the weak group inverse (called as the WG inverse in the present paper) for square complex matrices of an arbitrary index, and give some of its characterizations and properties. Furthermore, we introduce two orde…
View article
On Groups of PL-homeomorphisms of the Real Line Open
Richard J. Thompson invented his group F in the 60s; it is a group full of surprises: it has a finite presentation with 2 generators and 2 relators, and a derived group that is simple; it admits a peculiar infinite presentation and has a l…
View article
Semisimplicial spaces Open
This is an exposition of homotopical results on the geometric realisation of semisimplicial spaces. We then use these to derive basic foundational results about classifying spaces of topological categories, possibly without units. The topi…
View article
Feathered gyrogroups and gyrogroups with countable pseudocharacter Open
Topological gyrogroups, with a weaker algebraic structure than groups, have been investigated recently. In this paper, we prove that every feathered strongly topological gyrogroup is paracompact, which implies that every feathered strongly…
View article
Weakly almost periodic functions, model-theoretic stability, and minimality of topological groups Open
We investigate the automorphism groups of $\\aleph\\_0$-categorical structures\nand prove that they are exactly the Roelcke precompact Polish groups. We show\nthat the theory of a structure is stable if and only if every Roelcke uniformly\…
View article
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…
View article
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…
View article
Topological Rough Groups Open
The concept of topological group is a simple combination of the concepts of abstract group and topological space. The purpose of this paper is to combine the concepts of topological space and rough groups; called topological rough groups o…
View article
Computable topological groups and Pontryagin duality Open
The well-known Pontryagin Duality (classically) reduces the study of compact abelian groups to the algebraic theory of discrete abelian groups. At first glance, Pontryagin Duality seems to be "algorithmic" in nature. Quite unexpectedly, th…
View article
Topological full groups of ample groupoids with applications to graph algebras Open
We study the topological full group of ample groupoids over locally compact spaces. We extend Matui’s definition of the topological full group from the compact to the locally compact case. We provide two general classes of étale groupoids …
View article
Free Boolean Topological Groups Open
Known and new results on free Boolean topological groups are collected. An account of the properties that these groups share with free or free Abelian topological groups and properties specific to free Boolean groups is given. Special emph…
View article
G-connectedness in topological groups with operations Open
It is a well known fact that for a Hausdorff topological group X, the limits of convergent sequences in X define a function denoted by lim from the set of all convergent sequences in X to X. This notion has been modified by Connor and Gros…
View article
Minimal subshifts of arbitrary mean topological dimension Open
Let $G$ be a countable infinite amenable group and $P$ be a polyhedron. We\ngive a construction of minimal subshifts of $P^G$ with arbitrarily mean\ntopological dimension less than $\\dim P$.\n
View article
Soft Topological Transformation Groups Open
The aim of the present study is to introduce the concept of soft topological transformation groups by examining the topological transformation groups, which are the core subject of algebraic topology under the soft approach. Actions of sof…
View article
Higher Categories and Topological Quantum Field Theories Open
We give a construction of Turaev-Viro type (3+1)-dimensional Topological Quantum Field Theory out of a G-crossed braided spherical fusion category for G a finite group. The resulting invariant of 4-manifolds generalizes several known invar…
View article
Topological Fundamental Groups and Small Generated Coverings Open
This paper is devoted to study some topological properties of the SG subgroup, π sg 1 (X, x), of the quasitopological fundamental group of a based space (X, x), π qtop 1 (X, x), its topological properties as a subgroup of the topological f…
View article
Additivity of higher rho invariants and nonrigidity of topological manifolds Open
Let $X$ be a closed oriented connected topological manifold of dimension $n\geq 5$. The structure group of $X$ is the abelian group of equivalence classes of all pairs $(f, M)$ such that $M$ is a closed oriented manifold and $f\colon M \to…
View article
Continuous Representability of Interval Orders: The Topological Compatibility Setting Open
In this paper, we go further on the problem of the continuous numerical representability of interval orders defined on topological spaces. A new condition of compatibility between the given topology and the indifference associated to the m…
View article
A variational principle of topological pressure on subsets for amenable group actions Open
In this paper, we establish a variational principle for topological pressure on compact subsets in the context of amenable group actions. To be precise, for a countable amenable group action on a compact metric space, say , for any potenti…
View article
Cohomogeneity one topological manifolds revisited Open
We prove a structure theorem for closed topological manifolds of cohomogeneity one; this result corrects an oversight in the literature. We complete the equivariant classification of closed, simply-connected cohomogeneity one topological m…
View article
Irresolute-topological groups Open
We introduce and study two classes of topologized groups, which are called here irresolute-topological and Irr-topological, investigate their properties, and establish their differences from topological groups. For this purpose we employ i…
View article
Bulk topology of line-nodal structures protected by space group symmetries in class AI Open
We give an exhaustive characterization of the topology of band structures in class AI, using nonsymmorphic space group 33 ($Pna2_1$) as a representative example where a great variety of symmetry protected line-nodal structures can be forme…
View article
On uniformly discrete subsets in uniform spaces and topological groups Open
On uniformly discrete subsets in uniform
View article
Automatic continuity for homeomorphism groups of noncompact manifolds Open
We extend the proof of automatic continuity for homeomorphism groups of manifolds to non-compact manifolds and manifolds with marked points and their mapping class groups. Specifically, we show that, for any manifold $M$ homeomorphic to th…
View article
Algebraic entropy on strongly compactly covered groups Open
We introduce a new class of locally compact groups, namely the strongly compactly covered groups, which are the Hausdorff topological groups G such that every element of G is contained in a compact open normal subgroup of G. For continuous…
View article
Locally Quasi-Convex Compatible Topologies on a Topological Group Open
For a locally quasi-convex topological abelian group (G,τ), we study the poset \(\mathscr{C}(G,τ)\) of all locally quasi-convex topologies on (G) that are compatible with (τ) (i.e., have the same dual as (G,τ) ordered by inclusion. Obvious…
View article
A locally quasi-convex abelian group without a Mackey group topology Open
We give the first example of a locally quasi-convex (even countable reflexive and $k_\omega$) abelian group $G$ which does not admit the strongest compatible locally quasi-convex group topology. Our group $G$ is the Graev free abelian grou…
View article
On some spaces via topological ideals Open
Our main purpose is to introduce and investigate the concepts of some forms of spaces via topological ideals. Some characterizations of some forms of spaces via topological ideals are established. Moreover, several properties of ⋆ \star …