Related papers: Skeletally generated spaces and absolutes

In this paper, we prove that, a compact complex manifold $X$ admits a smooth Hermitian metric with positive (resp. negative) scalar curvature if and only if $K_X$ (resp. $K_X^{-1}$) is not pseudo-effective. On the contrary, we also show…

Algebras generated by strictly positive matrices are described up to similarity, including the commutative, simple, and semisimple cases. We provide sufficient conditions for some block diagonal matrix algebras to be generated by a set of…

We study the class of compact spaces that appear as structure spaces of separable Banach lattices. In other words, we analyze what $C(K)$ spaces appear as principal ideals of separable Banach lattices. Among other things, it is shown that…

A smooth compactification X<n> of the configuration space of n distinct labeled points in a smooth algebraic variety X is constructed by a natural sequence of blowups, with the full symmetry of the permutation group S_n manifest at each…

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.

It is shown that the Schreier space X admits a set of continuum cardinality whose elements are mutually incomparable complemented subspaces spanned by subsequences of the natural Schauder basis of X.

Given an arbitrary spectral space $X$, we endow it with its specialization order $\leq$ and we study the interplay between suprema of subsets of $(X,\leq)$ and the constructible topology. More precisely, we investigate about when the…

Let G be a finite group. The stable module category of G has been applied extensively in group representation theory. In particular, it has been used to great effect that it is a triangulated category which is compactly generated. Let H be…

It is well-known that a finitely generated group $\Gamma$ has Kazhdan's property (T) if and only if the Laplacian element $\Delta$ in ${\mathbb R}[\Gamma]$ has a spectral gap. In this paper, we prove that this phenomenon is witnessed in…

We consider rigidity properties of compact symmetric spaces $X$ with metric $g_0$ of rank one. Suppose $g$ is another Riemannian metric on $X$ with sectional curvature $\kappa$ bounded by $0 \leq \kappa \leq 1$. If $g$ equals $g_0$ outside…

A characterization of $\varkappa$-metrizable compacta in terms of extension of functions and usco retractions into superextensions is established.

We prove the following. Let $R$ be a Noetherian ring, $B$ a finitely generated $R$-algebra, and $A$ a pure $R$-subalgebra of $B$. Then $A$ is finitely generated over $R$.

If kappa is strongly compact, lambda > kappa is regular, then (2^{< lambda})^+ --> (lambda+eta)^2_theta holds for eta,theta<kappa.

Graphons are analytic objects associated with convergent sequences of graphs. Problems from extremal combinatorics and theoretical computer science led to a study of graphons determined by finitely many subgraph densities, which are…

We introduce a general method of constructing locally compact scattered spaces from certain families of sets and then, with the help of this method, we prove that if kappa^{<kappa}=kappa then there is such a space of height kappa^+ with…

A space $X$ is submaximal if any dense subset of $X$ is open. In this paper, we prove that every submaximal topological gyrogroup of non-measurable cardinality is strongly $\sigma$-discrete. Moreover, we prove that every submaximal strongly…

We construct a combinatorial moduli space closely related to the KSV-compactification of the moduli space of bordered marked Riemann surfaces. The open part arises from symmetric metric ribbon graphs. The compactification is obtained by…

The paper describes the algebraic structure of the graded algebra of differentially homogeneous polynomials of fixed finite order. We show that it is a finitely generated algebra, and we exhibit a minimal set of generators. Along the way,…

Let $X$ be a set of cardinality $\kappa$ such that $\kappa^\omega=\kappa$. We prove that the linear algebra $\mathbb{R}^X$ (or $\mathbb{C}^X$) contains a free linear algebra with $2^\kappa$ generators. Using this, we prove several…

In a recent paper \cite{T} the fact that a class of locally compact metric spaces $X$, among which are Euclidean spaces, are not homemorphic to their punctured version $X\men\{p\}$, was given an interesting new proof which does not use…