Related papers: Openly factorizable spaces and compact extensions …

We give an interpretation of the semi-infinite intersection cohomology sheaf associated to a semisimple simply-connected algebraic group in terms of finite-dimensional geometry. Specifically, we describe a procedure for building…

In this note, we consider the space $H(\Omega)^{\mathbb N}$ of sequences of holomorphic functions on an open set $\Omega\subset {\mathbb C}$. If $H(\Omega)$ is endowed with its natural topology and $H(\Omega)^{\mathbb N}$ is endowed with…

For an affine spherical homogeneous space G/H of a connected semisimple algebraic group G, we consider the factorization morphism by the action on G/H of a maximal unipotent subgroup of G. We prove that this morphism is equidimensional if…

Characterizations of paracompact finite $C$-spaces via continuous selections are given. We apply these results to obtain some properties of finite $C$-spaces. Factorization theorems and a completion theorem for finite $C$- spaces are also…

A locally compact group $G$ has the factorization property if the map $$C^*(G)\odot C^*(G)\ni a\otimes b\mapsto \lambda(a)\rho(b)\in\mathcal B(L^2(G))$$ is continuous with respect to the minimal C*-norm. This paper seeks to initiate a…

In this paper we show that the six functor formalism for sheaves on locally compact Hausdorff topological spaces, as developed for example in Kashiwara and Schapira's book Sheaves on Manifolds, can be extended to sheaves with values in any…

In this article we study definable functions in tame expansions of algebraically closed valued fields. For a given definable function we have two types of results: of type (I), which hold at a neighborhood of infinity, and of type (II),…

In this note we extend two characterizations of admissible operators with respect to $\mathrm{L}^p$ to more general Orlicz spaces. The equivalent conditions are given by the property that an associated operator generates a strongly…

We study topologization of the semigroup $\mathscr{O\!\!I}\!_n(L)$ of finite partial order isomorphisms of a bounded rank of an infinite linear ordered set $(L,\leqslant)$. In particular we show that every $T_1$ left-topological…

We consider the Fourier-Stietljes algebra B(G) of a locally compact group G. We show that operator amenablility of B(G) implies that a certain semitolpological compactification of G admits only finitely many idempotents. In the case that G…

In this work we characterize those shift spaces which can support a 1-block quasi-group operation and show the analogous of Kitchens result: any such shift is conjugated to a product of a full shift with a finite shift. Moreover, we prove…

The aim of this paper is to continue the study of sg-compact spaces. The class of sg-compact spaces is a proper subclass of the class of hereditarily compact spaces. In our paper we shall consider sg-compactness in product spaces. Our main…

It is proved that any countable index, universally measurable subgroup of a Polish group is open. By consequence, any universally measurable homomorphism from a Polish group into the infinite symmetric group $S_\infty$ is continuous. It is…

We prove that if a pair of semi-cosimplicial spaces (X,Y) arise from a coloured operad then the semi-totalization sTot(Y) has the homotopy type of a relative double loop space and the pair (sTot(X),sTot(Y)) is weakly equivalent to an…

Let $\mathfrak{P}$ be a topological property. We study the relation between the order structure of the set of all $\mathfrak{P}$-extensions of a completely regular space $X$ with compact remainder (partially ordered by the standard partial…

In this paper the notion of $\infty$-open-multicommutativity of functors in the category of compact Hausdorff spaces is considered. This property is a generalization of the open-multicommutativity on the case of infinite diagrams. It is…

If $\mathcal P$ is a family of filters over some set $I$, a topological space $X$ is \emph{sequencewise $\mathcal P$-\brfrt compact} if, for every $I$-indexed sequence of elements of $X$, there is $F \in \mathcal P$ such that the sequence…

We introduce and investigate a topological version of St\"ackel's 1907 characterization of finite sets, with the goal of obtaining an interesting notion that characterizes usual compactness (or a close variant of it). Define a $T_2$…

Semigroup actions and their invertible extensions are discussed. First, we develop a theory of natural extensions for continuous actions of countable, embeddable semigroups. Second, we demonstrate that not every surjective such action of a…

For any affine semigroup $S$ the set $S\cup\{\infty\}$ has a natural structure of semigroup, additionally if $S$ is endowed with the discrete topology, the semigroup $S\cup\{\infty\}$ can be studied as the one-point compactification of $S$.…