T. Banakh

activity

20062025

most citedEmbedding the bicyclic semigroup into countably compact topological semigroups

33 citations · 687 across the 231 of their papers we have counts for

collaborators

Showing 2018 · math.GNShow all

12 papers · 2 filters

math.GN2018★ 5 cited

The normality and bounded growth of balleans

Taras Banakh, Igor Protasov

By a ballean we understand a set $X$ endowed with a family of entourages which is a base of some coarse structure on $X$ . Given two unbounded ballean $X, Y$ with normal product $X\t…

math.GN2018

The continuity of Darboux injections between manifolds

Iryna Banakh, Taras Banakh

We prove that an injective map $f : X \to Y$ between connected metrizable spaces $X, Y$ is continuous if for every connected subset $C \subset X$ the image $f (C)$ is connected and one o…

math.GN2018

A parallel metrization theorem

Taras Banakh, Olena Hryniv

Two non-empty sets $A, B$ of a metric space $(X, d)$ are called parallel if $d (a, B) = d (A, B) = d (A, b)$ for any points $a \in A$ and $b \in B$ . Answering a question posed on Mathoverflow, w…

math.GN2018

Haar-open sets: a right way of generalizing the Steinhaus sum theorem to non-locally compact groups

Taras Banakh

Let $X$ be the countable product of Abelian locally compact Polish groups and $A, B \subset X$ be two Borel sets, which are not Haar-null in $X$ . We prove that the sum-set $A+B:=\{a+…

math.GN2018★ 9 cited

Complete topologized posets and semilattices

Taras Banakh, Serhii Bardyla

In this paper we discuss the notion of completeness of topologized posets and survey some recent results on closedness properties of complete topologized semilattices.

math.GN2018★ 10 cited

The closedness of complete subsemilattices in functionally Hausdorff semitopological semilattices

Taras Banakh, Serhii Bardyla, Alex Ravsky

A topologized semilattice $X$ is complete if each non-empty chain $C \subset X$ has $in f C \in C ˉ$ and $sup C \in C ˉ$ . It is proved that for any complete subsemilattice $X$ of…

math.GN2018★ 6 cited

On images of complete topologized subsemilattices in sequential semitopological semilattices

Taras Banakh, Serhii Bardyla

A topologized semilattice $X$ is called complete if each non-empty chain $C \subset X$ has $in f C \in C ˉ$ and $sup C \in C ˉ$ . We prove that for any continuous homomorphism $h:…

math.GN2018★ 1 cited

The continuity of additive and convex functions, which are upper bounded on non-flat continua in $R^{n}$

Taras Banakh, Eliza Jabłońska, Wojciech Jabłoński

We prove that for a continuum $K \subset R^{n}$ the sum $K^{+ n}$ of $n$ copies of $K$ has non-empty interior in $R^{n}$ if and only if $K$ is not flat in the sense that…

math.GN2018★ 20 cited

Metrizable quotients of $C_{p}$ -spaces

T. Banakh, J. Kąkol, W. Śliwa

The famous Rosenthal-Lacey theorem asserts that for each infinite compact set $K$ the Banach space $C (K)$ admits a quotient which is either a copy of $c$ or $ℓ_{2}$ . What is the…

math.GN2018★ 6 cited

The interplay between weak topologies on topological semilattices

Taras Banakh, Serhii Bardyla

We study the interplay between three weak topologies on a topological semilattice $X$ : the weak $^{\circ}$ topology $W_{X}^{\circ}$ (generated by the base consiting of open subse…

math.GN2018

Realizing spaces as path-component spaces

Taras Banakh, Jeremy Brazas

The path component space of a topological space $X$ is the quotient space $π_{0} (X)$ whose points are the path components of $X$ . We show that every Tychonoff space $X$ is the path-c…

math.GN2018★ 3 cited

Haar- $I$ sets: looking at small sets in Polish groups through compact glasses

Taras Banakh, Szymon Głąb, Eliza Jabłońska +1

Generalizing Christensen's notion of a Haar-null set and Darji's notion of a Haar-meager set, we introduce and study the notion of a Haar- $I$ set in a Polish group. Here $…

The normality and bounded growth of balleans

The continuity of Darboux injections between manifolds

A parallel metrization theorem

Haar-open sets: a right way of generalizing the Steinhaus sum theorem to non-locally compact groups

Complete topologized posets and semilattices

The closedness of complete subsemilattices in functionally Hausdorff semitopological semilattices

On images of complete topologized subsemilattices in sequential semitopological semilattices

The continuity of additive and convex functions, which are upper bounded on non-flat continua in Rn

Metrizable quotients of Cp​-spaces

The interplay between weak topologies on topological semilattices

Realizing spaces as path-component spaces

Haar-I sets: looking at small sets in Polish groups through compact glasses

The continuity of additive and convex functions, which are upper bounded on non-flat continua in $R^{n}$

Metrizable quotients of $C_{p}$ -spaces

Haar- $I$ sets: looking at small sets in Polish groups through compact glasses