Related papers: Closed subsets of compact-like topological spaces

Let $\kappa$ be an infinite cardinal. A topological space $X$ is $\kappa$-bounded if the closure of any subset of cardinality $\le\kappa$ in $X$ is compact. We discuss the problem of embeddability of topological spaces into Hausdorff…

The kth finite subset space of a topological space X is the space exp_k X of non-empty finite subsets of X of size at most k, topologised as a quotient of X^k. The construction is a homotopy functor and may be regarded as a union of…

The aim of this paper is to study the topological properties of some classes of subsemimodules endowed with a subbasis closed-set topology. We show that such spaces are $T_0$. When the semimodule is finitely generated, those spaces are…

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…

Let $\mathcal C$ be a class of $T_1$ topological semigroups, containing all Hausdorff zero-dimensional topological semigroups. A semigroup $X$ is $\mathcal C$-$closed$ if $X$ is closed in any topological semigroup $Y\in\mathcal C$ that…

Let $\mathcal C$ be a class of topological semigroups. A semigroup $X$ is $injectively$ $\mathcal C$-$closed$ if $X$ is closed in each topological semigroup $Y\in\mathcal C$ containing $X$ as a subsemigroup. Let $\mathsf{T_{\!2}S}$ (resp.…

Two non-discrete Hausdorff group topologies $\tau, \delta$ on a group $G$ are called {\it transversal} if the least upper bound $\tau\vee \delta$ of $\tau$ and $\delta$ is the discrete topology. In this paper, we discuss the existence of…

A class of almost paratopological groups is introduced, which (1) contains paratopological groups and Hausdorff quasitopological groups; (2) is closed under products; (3) subgroups. Almost paratopological $T_1$ groups $G$ are characterized…

Let $\mathcal C$ be a class of topological semigroups. A semigroup $X$ is called $absolutely$ $\mathcal C$-$closed$ if for any homomorphism $h:X\to Y$ to a topological semigroup $Y\in\mathcal C$, the image $h[X]$ is closed in $Y$. Let…

A topological semigroup is monothetic provided it contains a dense cyclic subsemigroup. The Koch problem asks whether every locally compact monothetic monoid is compact. This problem was opened for more than sixty years, till in 2018…

In the paper we study (countably) compact and (absolutely) $H$-closed primitive topological inverse semigroups. We describe the structure of compact and countably compact primitive topological inverse semigroups and show that any countably…

A subspace Y of a separable metrizable space X is separable, but without X metrizable this is not true even If Y is a closed linear subspace of a topological vector space X. K.H. Hofmann and S.A. Morris introduced the class of pro-Lie…

We study the problem of topologically order-embedding a given topological poset X in the space of all closed subsets of X which is topologized by the Fell topology and ordered by set inclusion. We show that this can be achieved whenever X…

We study the structure of inverse primitive feebly compact semitopological and topological semigroups. We find conditions when the maximal subgroup of an inverse primitive feebly compact semitopological semigroup $S$ is a closed subset 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…

The concept of `topological right transversal' is introduced to study right transversals in topological groups. Given any right quasigroup $S$ with a Tychonoff topology $T$, it is proved that there exists a Hausdorff topological group in…

The note contains a few results related to separation axioms and automatic continuity of operations in compact-like semitopological groups. In particular, is presented a semiregular semitopological group $G$ which is not $T_3$. We show that…

We define a notion of a rotund quasi-uniform space and describe a new direct construction of a (right-continuous) quasi-pseudometric on a (rotund) quasi-uniform space. This new construction allows to give alternative proofs of several…

The topology of the embedding of the coadjoint orbits of the unitary group U(H) of an in-finite dimensional complex Hilbert space H, as canonically determined subsets of the B-space T_s of symmetric trace class operators, is investigated.…

For a compact Hausdorff abelian group K and its subgroup H, one defines the g-closure g(H) of H in K as the subgroup consisting of $\chi \in K$ such that $\chi(a_n)\longrightarrow 0$ in T=R/Z for every sequence {a_n} in $\hat K$ (the…