Related papers: Skeletally generated spaces and absolutes

We introduce and investigate the class of skeletally Dugundji spaces as a skeletal analogue of Dugundji space. The main result states that the following conditions are equivalent for a given space $X$: (i) $X$ is skeletally Dugundji; (ii)…

A space has $\sigma$-compact tightness if the closures of $\sigma$-compact subsets determines the topology. We consider a dense set variant that we call densely k-separable. We consider the question of whether every densely k-separable…

We show that $X^\lambda$ is strongly homogeneous whenever $X$ is a non-separable zero-dimensional metrizable space and $\lambda$ is an infinite cardinal. This partially answers a question of Terada, and improves a previous result of the…

Over an associative ring we consider a class $\mathbb{X}$ of left modules which is closed under set-indexed coproducts and direct summands. We investigate when the triangulated homotopy category $\mathsf{K}(\mathbb{X})$ is compactly…

For a cardinal $\kappa > \omega$ a metric space $X$ is called to be $\kappa$-superuniversal whenever for every metric space $Y$ with $|Y| < \kappa$ every partial isometry from a subset of $Y$ into $X$ can be extended over the whole space…

We consider the following variation of the Scarborough-Stone problem: Is $X^\kappa$ always countably compact whenever $X$ is separable and sequentially compact?

All spaces are assumed to be Tychonoff. Given a realcompact space $X$, we denote by $\mathsf{Exp}(X)$ the smallest infinite cardinal $\kappa$ such that $X$ is homeomorphic to a closed subspace of $\mathbb{R}^\kappa$. Our main result shows…

A topological space $X$ is called hereditarily supercompact if each closed subspace of X is supercompact. By a combined result of Bula, Nikiel, Tuncali, Tymchatyn, and Rudin, each monotonically normal compact Hausdorff space is hereditarily…

We give a partial solution to a question by Alas, Junqueria and Wilson by proving that under PFA the one-point compactification of a locally compact, discretely generated and countably tight space is also discretely generated. After this,…

We show that a linearly ordered topological space is initially \lambda-compact if and only if it is \lambda-bounded, that is, every set of cardinality $\leq \lambda$ has compact closure. As a consequence, every product of initially…

We establish some geometrical properties of the space of idempotent probability measures. In particular, for a compact $X$ it is established that if the space $I_{3}(X)\backslash X$ is hereditary normally, then $X$ is metrizable; some…

For any countable $CW$-complex $K$ and a cardinal number $\tau\geq\omega$ we construct a completely metrizable space $X(K,\tau)$ of weight $\tau$ with the following properties: $\e X(K,\tau)\leq K$, $X(K,\tau)$ is an absolute extensor for…

Let $k$ be a field. We characterize the group schemes $G$ over $k$, not necessarily affine, such that $\mathsf{D}_{\mathrm{qc}}(B_kG)$ is compactly generated. We also describe the algebraic stacks that have finite cohomological dimension in…

In \cite{Chaber}, Chaber has proved that countably compact spaces with a quasi $G_{\delta }$-diagonal are compact. We prove that initially $\kappa $% -compact spaces with a quasi $G_{\kappa }$-diagonal are compact, for any infinite cardinal…

A Tychonoff space $X$ is called $\kappa$-pseudocompact if for every continuous mapping $f$ of $X$ into $\mathbb{R}^\kappa$ the image $f(X)$ is compact. This notion generalizes pseudocompactness and gives a stratification of spaces lying…

We show that there are locally compact spaces that can be condensed onto separable spaces but not onto compact separable spaces. We also show that for every cardinal $\kappa$ there is a locally compact topological group of cardinality…

Skeletal polyhedra and polygonal complexes are finite or infinite periodic structures in 3-space with interesting geometric, combinatorial, and algebraic properties. These structures can be viewed as finite or infinite periodic graphs…

A topological space $X$ is called strongly $\sigma$-metrizable if $X=\bigcup_{n\in\omega}X_n$ for an increasing sequence $(X_n)_{n\in\omega}$ of closed metrizable subspaces such that every convergence sequence in $X$ is contained in some…

Let B(kappa, lambda) be the subalgebra of P(kappa) generated by [kappa]^{<= lambda}. It is shown that if B is any homomorphic image of B(kappa, lambda) then either |B|< 2^lambda or |B|=|B|^lambda, moreover if X is the Stone space of B then…

Skeletal polyhedra are discrete connected structures consisting of finite (planar or skew) or infinite (linear, planar, or spatial) polygons as faces, with two faces on each edge and a circular vertex figure at each vertex. The present…