Related papers: Embeddings into countably compact Hausdorff spaces

In our previous paper [9], we have introduced topological nearly entropy, Ent_N (f) by restricting X into a class of nearly compact spaces. In the present paper, some additional properties of this notion are studied. Furthermore, we…

We study the spaces of embeddings of manifolds in a Euclidean space. More precisely we look at the homotopy fiber of the inclusion of these spaces to the spaces of immersions. As a main result we express the rational homotopy type of…

It is shown that if a $T_2$ topological space $X$ contains a closed uncountable discrete subspace, then the spaces $(\omega_1 + 1)^{\omega}$ and $(\omega_1 + 1)^{\omega_1}$ embed into $(CL(X),\tau_F)$, the hyperspace of nonempty closed…

In this paper, an estimation of lower bound of topological entropy for coupled-expanding systems associated with transition matrices in compact Hausdorff spaces is given. Estimations of upper and lower bounds of topological entropy for…

Recently many papers on cone metric spaces have been appeared, and main topological properties of such spaces have been obtained. A cone metric space is Hausdorff, and first countable, so the topology of it coincides with a topology induced…

We determine the excluded minors characterising the class of countable graphs that embed into some compact surface.

We introduce two notions of a contractive orbit of a set-valued map defined in a first countable space. The first defines the contraction with respect to the topology of the underlying space while the second defines the contraction with…

The study of embeddings of smooth manifolds into Euclidean and projective spaces has been for a long time an important area in topology. In this paper we obtain improvements of classical results on embeddings of smooth manifolds, focusing…

The aim of this paper is to introduce and give preliminary investigation of T-locally compact spaces. Locally compact and T-locally compact are independent of each other. Every Hausdorff, locally compact space is T-locally compact.…

Urysohn constructed a separable complete universal metric space homogeneous for all finite subspaces, which is today called the Urysohn universal metric space. Some authors have recently investigated an ultrametric analogue of this space.…

Represented spaces form the general setting for the study of computability derived from Turing machines. As such, they are the basic entities for endeavors such as computable analysis or computable measure theory. The theory of represented…

Compact sets in constructive mathematics capture our intuition of what computable subsets of the plane (or any other complete metric space) ought to be. A good representation of compact sets provides an efficient means of creating and…

We introduce the notion of coupled embeddability, defined for maps on products of topological spaces. We use known results for nonsingular biskew and bilinear maps to generate simple examples and nonexamples of coupled embeddings. We study…

For many years, there have been conducting research (e.g. by Bergelson, Furstenberg, Kojman, Kubi\'{s}, Shelah, Szeptycki, Weiss) into sequentially compact spaces that are, in a sense, topological counterparts of some combinatorial…

Below, by space we mean a separable metrizable zero-dimensional space. It is studied when the space can be embedded in a Cantor set while maintaining the algebraic structure. Main results of the work: every space is an open retract of a…

It is shown that any bounded metric space can be isometrically embedded into the Gromov--Hausdorff metric class GH. This result is a consequence of local geometry description of the class GH in a sufficiently small neighborhood of a generic…

The aim of this paper is to introduce a new weak separation axiom that generalizes the separation properties between $T_1$ and completely Hausdorff. We call a topological space $(X,\tau)$ a $T_{\kappa,\xi}$-space if every compact subset of…

In this manuscript, we claim that the newly introduced $\mathcal{F}$-metric spaces are Hausdorff and also first countable. Moreover, we assert that every separable $\mathcal{F}$-metric space is second countable. Additionally, we acquire…

We show that compact Riemannian manifolds, regarded as metric spaces with their global geodesic distance, cannot contain a number of rigid structures such as (a) arbitrarily large regular simplices or (b) arbitrarily long sequences of…

Using an iterative tree construction we show that for simple computable subsets of the Cantor space Hausdorff, constructive and computable dimensions might be incomputable.