Related papers: Locally Connected HL Compacta

We further investigate the weak topology generated by the irreducible unitary representations of a group $G$. A deep result due to Ernest \cite{Ernest1971} and Hughes \cite{Hughes1973} asserts that every weakly compact subset of a locally…

We introduce the concept of hereditarily non uniformly perfect sets, compact sets for which no compact subset is uniformly perfect, and compare them with the following: Hausdorff dimension zero sets, logarithmic capacity zero sets, Lebesgue…

We prove that each non-metrizable sequential rectifiable space $X$ of countable $cs^*$-character contains a clopen rectifiable submetrizable $k_\omega$-subspace $H$ and admits an open disjoint cover by subspaces homeomorphic to clopen…

A topological space $G$ is said to be a {\it rectifiable space} provided that there are a surjective homeomorphism $\phi :G\times G\rightarrow G\times G$ and an element $e\in G$ such that $\pi_{1}\circ \phi =\pi_{1}$ and for every $x\in G$…

Let G be a locally compact group, and let U be its unitary representation on a Hilbert space H. Endow the space L(H) of linear bounded operators on H with weak operator topology. We prove that if U is a measurable map from G to L(H) then it…

In this note we show that a connected, closed and locally convex subset (with an extra assumption on the diameter with respect to the induced length metric if $\kappa>0$) of a $CAT(\kappa)$ space is convex.

As proven in a celebrated theorem due to Vaisman, pure locally conformally K\"ahler metrics do not exist on compact K\"ahler manifolds. In a previous paper, we extended this result to the singular setting, more precisely to K\"ahler spaces…

We prove injectivity of the canonical map from singular homology to measure homology for certain ``mildly wild" spaces, that is, certain spaces not having the homotopy type of a CW-complex, but having countable fundamental groups.

We will discuss in this paper homogeneous locally conformally Keahler (or shortly homogeneous l.c.K.) manifolds and locally homogeneous l.c.K. manifolds from various aspects of study in the field of l.c.K. geometry. We will provide a survey…

The class of $L\Sigma(\leq\omega)$-spaces was introduced in 2006 by Kubi\'s, Okunev and Szeptycki as a natural refinement of the classical and important notion of Lindel\"of $\Sigma$-spaces. Compact $L\Sigma(\leq\omega)$-spaces were…

The complex projective structures considered is this article are compact curves locally modeled on $\mathbb{CP}^1$. To such a geometric object, modulo marked isomorphism, the monodromy map associates an algebraic one: a representation of…

We present a complete classification of Hausdorff locally compact polycyclic monoids up to a topological isomorphism. A {\em polycyclic monoid} is an inverse monoid with zero, generated by a subset $\Lambda$ such that $xx^{-1}=1$ for any…

We study the isomorphism relation on Borel classes of locally compact Polish metric structures. We prove that isomorphism on such classes is always classifiable by countable structures (equivalently: Borel reducible to graph isomorphism),…

Localized noncommutative structures for manifolds with connection are constructed based on the use of vertical star products. The model's main feature is that two points that are far away from each other will not be subject to a deviation…

If a Peano continuum $X$ is semilocally simply connected, then it has a finite polyhedral approximation whose fundamental group is isomorphic to that of $X$. In general, this fails to be true. It is known that the fundamental group of a…

K. Kuperberg found a locally connected, finite-dimensional continuum which is homogeneous but not bihomogeneous. We give a similar but simpler example. Like previous constructions, the example is locally a Cartesian product of Menger…

We announce and examine the conjecture that each infinite connected normal Hausdorff space has a quotient homeomorphic to the unit interval, shown to be true with the additional assumption of compactness or local connectedness. Some…

A locally conformally K\"ahler (LCK) manifold is a manifold which is covered by a K\"ahler manifold, with the deck transform group acting by homotheties. We show that the search for LCK metrics on Oeljeklaus-Toma manifolds leads to a (yet…

We describe a family of locally conformal Kaehler metrics on class 1 Hopf surfaces H containing some recent metrics constructed by P. Gauduchon and L. ornea. We study some canonical foliations associated to these metrics, in particular a…

A space Y is called an extension of a space X if Y contains X as a dense subspace. An extension Y of X is called a one-point extension if Y-X is a singleton. Compact extensions are called compactifications and connected extensions are…