Related papers: Classifying locally compact semitopological polycy…

In this paper we study the semigroup $\mathscr{I}_{\infty}^{\nearrow}(\mathbb{N})$ of partial cofinal monotone bijective transformations of the set of positive integers $\mathbb{N}$. We show that the semigroup…

We show that for any connected smooth manifold $M$ of dimension different from $3$ the restriction of the compact-open topology to the diffeomorphism group of $M$ is minimal, i.e. the group does not admit a strictly coarser Hausdorff group…

Consider the following generalization of the bicyclic monoid. Let $\kappa$ be any infinite cardinal and let $\mathcal{IP\!F}\left(\sigma{\mathbb{N}^\kappa}\right)$ be the semigroup of all order isomorphisms between principal filters of the…

We extend the work of M. Rubin on locally moving groups to clones, showing that a locally moving polymorphism clone has automatic homeomorphicity with respect to the class of all polymorphism clones. We show that if…

The partial automorphism monoid of an inverse semigroup is an inverse monoid consisting of all isomorphisms between its inverse subsemigroups. We prove that a tightly connected fundamental inverse semigroup $S$ with no isolated nontrivial…

We establish a local model for the moduli space of holomorphic symplectic structures with logarithmic poles, near the locus of structures whose polar divisor is normal crossings. In contrast to the case without poles, the moduli space is…

We construct Morse homology groups associated with any regular function on a smooth complex algebraic variety, allowing singular and non-compact critical loci. These groups are generated by critical points of a certain large pertubation of…

Let X be a zero-dimensional compact space such that all non-empty clopen subsets of X are homeomorphic to each other, and let H(X) be the group of all self-homeomorphisms of X with the compact-open topology. We prove that the Roelcke…

A topological space is almost locally compact if it contains a dense locally compact subspace. We generalize a result from \cite{Ma}, showing that isomorphism on Borel classes of almost locally compact Polish metric structures is always…

In this paper we address the classification problem for locally compact (n-1)-connected CW-complexes with dimension less or equal than n+2 up to proper homotopy type. We obtain complete classification theorems in terms of purely algebraic…

Let $R\subseteq \Bbb Q$ be a subring of the rationals and let $p$ be the least prime (if none, $p=\infty $) which is not invertible in $R.$ For an $R$-local $r$-connected $CW$-complex $X$ of dimension $\leq \min(r+2p-3,rp-1), r\geq 1, $ a…

The symmetric inverse semigroup $I(X)$ on a set $X$ is the collection of all partial bijections between subsets of $X$ with composition as the algebraic operation. We study a minimal Hausdorff inverse semigroup topologies on $I(X)$. When…

This paper continues our investigation into the question of when a homotopy $\omega = \{\omega_t\}_{t \in [0,1]}$ of 2-cocycles on a locally compact Hausdorff groupoid $\mathcal{G}$ gives rise to an isomorphism of the $K$-theory groups of…

We show that a topological semigroup of finite partial bijections $\mathscr{I}_\lambda^n$ of an infinite set with a compact subsemigroup of idempotents is absolutely $H$-closed and any countably compact topological semigroup does not…

Every locally compact local group is locally isomorphic to a topological group.

In this paper we explore the extent to which the algebraic structure of a monoid $M$ determines the topologies on $M$ that are compatible with its multiplication. Specifically we study the notions of automatic continuity; minimal Hausdorff…

Let $X$ be a locally symmetric space $\Gamma\backslash G/K$ where $G$ is a connected non-compact semisimple real Lie group with trivial centre, $K$ is a maximal compact subgroup of $G$, and $\Gamma\subset G$ is a torsion-free irreducible…

The Ehresmann-Schein-Nambooripad theorem gives a structure theorem for inverse monoids: they are inductive groupoids. A particularly nice case due to Jarek is that commutative inverse monoids become semilattices of abelian groups. It has…

We study the general form of isomorphisms on the algebra of compactly supported complex-valued continuous functions defined on a locally compact Hausdorff space (the proof of which works for the algebra of $C^k-$differentiable functions on…

We present an expository overview of the monoidal structures in the category of linearly compact vector spaces. Bimonoids in this category are the natural duals of infinite-dimensional bialgebras. We classify the relations on words whose…