Related papers: Group topologies coarser than the Isbell topology

Let $X$ be a completely regular topological space. We assign to each (set theoretic) ideal of $X$ an (algebraic) ideal of $C_B(X)$, the normed algebra of continuous bounded complex valued mappings on $X$ equipped with the supremum norm. We…

We extend the Dikranjan-Uspenskij notions of c-compact and h-complete topological group to the morphism level, study the stability properties of the newly defined types of maps, such as closure under direct products, and compare them with…

We prove that the semigroup operation of a topological semigroup $S$ extends to a continuous semigroup operation on its the Stone-\v{C}ech compactification $\beta S$ provided $S$ is a pseudocompact openly factorizable space, which means…

A natural topology on the space of left orderings of an arbitrary semi-group is introduced. It is proved that this space is compact and that for free abelian groups it is homeomorphic to the Cantor set. An application of this result is a…

In this paper, plane polynomial systems having a singular point attracting all orbits in positive time are classified up to topological equivalence. This is done by assigning a combinatorial invariant to the system (a so-called "feasible…

We introduce the notion of an R-group of which the clas- sical groups R, Z and R_+ are typical examples, and we study flows (X;H), where X is a locally compact space and H is a continuous R- group action on X with the further property that…

Without assuming the field structure on the additive group of real numbers $\mathbb{R}$ with the usual order $<,$ we explore the fact that every proper subgroup of $\mathbb{R}$ is either closed or dense. This property of subgroups of the…

By definition, the intersection of finitely many open sets of any topological space is open. Nachbin observed that, more generally, the intersection of compactly many open sets is open. Moreover, Nachbin applied this to obtain elegant…

We show that the strong operator topology, the weak operator topology and the compact-open topology agree on the space of unitary operators of a infinite dimensional separable Hilbert space. Moreover, we show that the unitary group endowed…

Given a measurable twisted action of a second-countable, locally compact group G on a separable C*-algebra A, we prove the existence of a topology on AxG making it a continuous bundle, whose cross sectional C*-algebra is isomorphic to the…

We introduce moment maps for continuous unitary representations of general topological groups. For solvable separable locally compact groups, we prove that the closure of the image of the moment map of any representation is convex.

We equip the product of countably many copies of a compact Abelian group X with the uniform topology, and study some properties of the topological group G thus obtained. In particular, we determine the cardinality of the dual group of G,…

In this paper we further study links between concentration of measure in topological transformation groups, existence of fixed points, and Ramsey-type theorems for metric spaces. We prove that whenever the group $\Iso(\U)$ of isometries of…

We introduce the Insertion Chain Complex, a higher-dimensional extension of insertion graphs, as a new framework for analyzing finite sets of words. We study its topological and combinatorial properties, in particular its homology groups,…

Any unital separable continuous C(X)-algebra with properly infinite fibres is properly infinite as soon as the compact Hausdorff space X has finite topolog-ical dimension. We study conditions under which this is still the case if the…

This paper forms the second part of a series by the authors [GMV1,GMV3] concerning the structure theory of nilspaces of Antol\'in Camarena and Szegedy. A nilspace is a compact space $X$ together with closed collections of cubes…

If X is a proper CAT(-1)-space and $\Gamma$ a non-elementary discrete group of isometries acting properly discontinuously on X, it is shown that the geodesic flow on the quotient space Y=X/$\Gamma$ is topologically mixing, provided that the…

A topological space is iso-dense if it has a dense set of isolated points. A topological space is scattered if each of its non-empty subspaces has an isolated point. In $\mathbf{ZF}$, in the absence of the axiom of choice, basic properties…

Being motivated by the study of the space $C_c(X)$ of all continuous real-valued functions on a Tychonoff space $X$ with the compact-open topology, we introduced in [15] the concepts of a $cp$-network and a $cn$-network (at a point $x$) in…

In this paper we put forward the definition of particular subsets on a unital C*-algebra, that we call isocones, and which reduce in the commutative case to the set of continuous non-decreasing functions with real values for a partial order…