Related papers: A combinatorial property of rho-functions

Let $X$ and $Y$ be the Hausdorff topological spaces and let $A$ be both an $\fs$- and $\gd$- subset of $X$. Let also $f\cn A\to Y$ be a function for which the inverse image of every open subset $U\subset Y$ is $\fs$ in $X$. We show that $f$…

A reduction of properties (invariants) of compact sets of real numbers to properties of countable orders is presented here. Discussed here is also an embedding property of some compact sets that are called t$\mathbb R$-sets. Among others,…

This paper investigates topological reconstruction, related to the reconstruction conjecture in graph theory. We ask whether the homeomorphism types of subspaces of a space $X$ which are obtained by deleting singletons determine $X$…

Let $Homeo(\Omega)$ be the group of all homeomorphisms of a Cantor set $\Omega$. We study topological properties of $Homeo(\Omega)$ and its subsets with respect to the uniform $(\tau)$ and weak $(\tau_w)$ topologies. The classes of…

Using the functor of Baumslag rationalization of groups we construct a functor on the category of all (non necessarily simply connected) spaces that extends the classical rationalization of simply connected spaces. We study this functor and…

A homeomorphism on a compact metric space is said hyper-expansive if every pair of different compact sets are separated by the homeomorphism in the Hausdorff metric. We characterize such dynamics as those with a finite number of orbits and…

Erd\H{o}s space $\mathfrak{E}$ and complete Erd\H{o}s space $\mathfrak{E}_c$ have been previously shown to have topological characterizations. In this paper, we provide a topological characterization of the topological space…

Transformation monoids carry a canonical topology --- the topology of point-wise convergence. A closed transformation monoid $\mathfrak{M}$ is said to have automatic homeomorphicity with respect to a class $\mathcal{K}$ of structures, if…

We study the combination of two o-minimal extensions of the theory of real closed fields: one by a T-convex subring and the other by a T-derivation. Let T be a complete, model complete o-minimal extension of RCF. We show that the combined…

Let $f$ and $g$ be scalar-valued, continuous functions on some topological space. We say that $g$ dominates $f$ in the compatibility ordering if $g$ coincides with $f$ on the support of $f$. We prove that two compact Hausdorff spaces are…

We describe the structure of ($0$-)simple inverse Hausdorff semitopological $\omega$-semigroups with compact maximal subgroups. In particular, we show that if $S$ is a simple inverse Hausdorff semitopological $\omega$-semigroup with compact…

We show that the topology of pointwise convergence on scattered spaces is compatible with the group structure of their homeomorphism group. We then establish a few topological properties of the homeomorphism group of the first uncountable…

For an $\alpha$-expansive homeomorphism of a compact space we give an elementary proof of the following well-known result in topological dynamics: A sufficient condition for the homeomorphism to have the shadowing property is that it has…

We show how to reconstruct the topology on the monoid of endomorphisms of the rational numbers under the strict or reflexive order relation, and the polymorphism clone of the rational numbers under the reflexive relation. In addition we…

For a closed topological manifold M with dim (M) >= 5 the topological structure set S(M) admits an abelian group structure which may be identified with the algebraic structure group of M as defined by Ranicki. If dim (M) = 2d-1, M is…

Let $f\colon M\to M$ be an expansive homeomorphism with dense topologically hyperbolic periodic points, $M$ a compact manifold. Then there is a local product structure in an open and dense subset of $M$. Moreover, if some topologically…

We show that every filter $\mathcal{F}$ on $\omega$, viewed as a subspace of $2^\omega$, is homeomorphic to $\mathcal{F}^2$. This generalizes a theorem of van Engelen, who proved that this holds for Borel filters.

T. Mostowski showed that every (real or complex) germ of an analytic set is homeomorphic to the germ of an algebraic set. In this paper we show that every (real or complex) analytic function germ, defined on a possibly singular analytic…

Let $X$ be a scheme. In this text, we extend the known definitions of a topology on the set $X(R)$ of $R$-rational points from topological fields, local rings and ad\`ele rings to any ring $R$ with a topology. This definition is functorial…

Let $X$ be a compact metric space and let $f:X\rightarrow X$ be a homeomorphism on $X$. We show that if $f$ is both pointwise recurrent and expansive, then the dynamical system $(X, f)$ is topologically conjugate to a subshift of some…