Related papers: Maximal (sequentially) compact topologies

Sequential parametrized topological complexity is a numerical homotopy invariant of a fibration, which arose in the robot motion planning problem with external constraints. In this paper, we study sequential parametrized topological…

We obtain necessary and sufficient conditions when a pseudocompact paratopological group is topological. (2-)pseudocompact and countably compact paratopological groups that are not topological are constructed. It is proved that each…

Let $M$ be an orientable connected closed surface and $f$ be an $R$-closed homeomorphism on $M$ which is isotopic to identity. Then the suspension of $f$ satisfies one of the following condition: 1) the closure of each element of it is…

We prove that each metrizable space (of cardinality less or equal to continuum) has a (first countable) uniform Eberlein compactification and each scattered metrizable space has a scattered hereditarily paracompact compactification. Each…

Here we extend the notion of target-local Gromov convergence of pseudoholomorphic curves to the case in which the target manifold is not compact, but rather is exhausted by compact neighborhoods. Under the assumption that the curves in…

In this survey, my aim has been to discuss the use of sequences and countable sets in general topology. In this way I have been led to consider five different classes of topological spaces: first countable spaces, sequential spaces, Frechet…

We obtain many results and solve some problems about feebly compact paratopological groups. We obtain necessary and sufficient conditions for such a group to be topological. One of them is the quasiregularity. We prove that each…

A Hausdorff topological group is called minimal if it does not admit a strictly coarser Hausdorff group topology. This paper mostly deals with the topological group $H_+(X)$ of order-preserving homeomorphisms of a compact linearly ordered…

We prove that the cohomology groups of a definably compact set over an o-minimal expansion of a group are finitely generated and invariant under elementary extensions and expansions of the language. We also study the cohomology of the…

We investigate closed subsets (subsemigroups, resp.) of compact-like topological spaces (semigroups, resp.). We prove that each Hausdorff topological space can be embedded as a closed subspace into an H-closed topological space. However,…

In this paper, it is shown that a topological space $X$ is compact iff every maximal ideal of the power set ring $\mathcal{P}(X)$ converges to exactly one point of $X$. Then as an application, simple and ring-theoretic proofs are provided…

Non-discrete semigroup $T_1$-topologies on the extended bicyclic semigroup $\mathscr{C}_\mathbb{Z}$ are constructed. Also, we present topological conditions, when a semigroup (shift-continuous) $T_1$-topology on $\mathscr{C}_\mathbb{Z}$ is…

We effectively bound T-singularities on non-rational projective surfaces with an arbitrary amount of T-singularities and ample canonical class. This fully generalizes the previous work for the case of one singularity, and illustrates the…

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

Using the notion of contiguity of simplicial maps, we adapt Farber's topological complexity to the realm of simplicial complexes. We show that, for a finite simplicial complex $K$, our discretized concept recovers the topological complexity…

We study global solutions to the thin obstacle problem with at most quadratic growth at infinity. We show that every ellipsoid can be realized as the contact set of such a solution. On the other hand, if such a solution has a compact…

We prove group existence and structure theorems in a general setting of tame topological theories. More precisely, we identify a linear/non-linear dividing line -- called topological 1-basedness -- among the class of t-minimal theories with…

We study directed sets definable in o-minimal structures, showing that in expansions of ordered fields these admit cofinal definable curves, as well as a suitable analogue in expansions of ordered groups, and furthermore that no analogue…

Topological mapping of a large physical system on a graph, and its decomposition using universal measures is proposed. We find inherent limits to the potential for optimization of a given system and its approximate representations by…

We study locally compact group topologies on semisimple Lie groups. We show that the Lie group topology on such a group $S$ is very rigid: every 'abstract' isomorphism between $S$ and a locally compact and $\sigma$-compact group $\Gamma$ is…