Wojciech Bielas

activity

20182025

collaborators

8 papers

math.GN2025

A solution to the problem of the existence of a dense plastic subset $X \subseteq R$ of cardinality $∣ X ∣ < c$

Wojciech Bielas

Under the assumption $c ⩾ ω_{2}$ , we give an example of a dense plastic subset $X \subseteq R$ of cardinality $∣ X ∣ < c$ . This answers Problem 1 of arXiv:251…

math.GN2025

On some modifications of the Niemytzki plane

Wojciech Bielas

We present a criterion that compares modifications of the Niemytzki plane. It follows that if usual tangent discs of the Niemytzki plane are replaced by triangles with bounded angl…

math.GN2023

On compact subsets of the reals

Wojciech Bielas, Mateusz Kula, Szymon Plewik

Motivated by results of J. R. Kline and R. L. Moore (1919) that a compact subset of the plane, homeomorphic to a subset of the reals, lies on the arc, we give a purely topological…

math.GN2022

Scattered $P$ -spaces of weight $ω_{1}$

Wojciech Bielas, Andrzej Kucharski, Szymon Plewik

We examine dimensional types of scattered $P$ -spaces of weight $ω_{1}$ . Such spaces can be embedded into $ω_{2}$ . There are established similarities between dimensional types of scatte…

math.GN2021

Dimensional types and P-spaces

Wojciech Bielas, Andrzej Kucharski, Szymon Plewik

We investigate the category of discrete topological spaces, with emphasis on inverse systems of height $ω_{1}$ . Their inverse limits belong to the class of $P$ -spaces, which allows u…

math.GN2021

A separate continuous function not feebly continuous

Wojciech Bielas

We construct a separate continuous function $f : Q \times Q \to [0, 1]$ and a dense subset $D \subseteq Q \times Q$ such that $f [D]$ is not dense in…

A solution to the problem of the existence of a dense plastic subset X⊆R of cardinality ∣X∣<c

On some modifications of the Niemytzki plane

On compact subsets of the reals

Scattered P-spaces of weight ω1​

Dimensional types and P-spaces

A separate continuous function not feebly continuous

A solution to the problem of the existence of a dense plastic subset $X \subseteq R$ of cardinality $∣ X ∣ < c$

Scattered $P$ -spaces of weight $ω_{1}$