Andrzej Kucharski
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Previous Organizations / Institutes
The organizations / institutes from the scholar's other articles in the past ten years
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Research Interests
Andrzej Kucharski has a total of 16 co-authors. Here are the top co-authors by number of shared publications:
- Sławomir Turek
Institute of Mathematics Cardinal Stefan Wyszynski Univwersity in Warsaw Warszawa POLAND
7 shared publications - Judyta Bąk
Institute of Mathematics , Jan Kochanowski University in Kielce , Świętokrzyska 15 25-406 , Kielce , Poland
4 shared publications - Marta Martynenko
Ivan Franko Natl Univ Lviv, Fac Mech & Math, UA-79000 Lvov, Ukraine
4 shared publications Sz. Plewik
4 shared publications- Szymon Plewik
Univ Silesia Katowice, Inst Math, Bankowa 14, PL-40007 Katowice, Poland
4 shared publications - Taras Banakh
Ivan Franko Univ Lviv, Lvov, Ukraine
4 shared publications
Latest Publications
- Open Access
A Knaster--Reichbach type theorem for graph structures
We study the properties of a generic object $\mathbb{P}$ in the category of finite graphs. It turns out that this object, being topologically a Cantor set, has the Knaster--Reichbach type property. Namely, every homeomorphism and isomorphism $h\colon K\to L$ where $K$ and $L$ are nowhere dense closed sets in $\mathbb{P}$ and consisting only of isolated vertices in $K$ and $L$ can be extended to the autohomeomorphism and autoisomorphism of the whole graph $\mathbb{P}$.Open AccessA Knaster--Reichbach type theorem for graph structures
We study the properties of a generic object $\mathbb{P}$ in the category of finite graphs. It turns out that this object, being topologically a Cantor set, has the Knaster--Reichbach type property. Namely, every homeomorphism and isomorphism $h\colon K\to L$ where $K$ and $L$ are nowhere dense closed sets in $\mathbb{P}$ and consisting only of isolated vertices in $K$ and $L$ can be extended to the autohomeomorphism and autoisomorphism of the whole graph $\mathbb{P}$. - Open Access
- 16 January 2025
- Published by Springer Nature in Results in Mathematics
- Vol. 80 (1) , 1-23
On Generic Topological Embeddings
We show that an embedding of a fixed 0-dimensional compact space K into the Čech–Stone remainder $$\omega ^*$$ as a nowhere dense P-set is the unique generic limit, a special object in the category consisting of all continuous maps from K to compact metric spaces. Using categorical Fraïssé theory, we obtain some well-known theorems about Čech–Stone remainders of infinite discrete spaces. Furthermore, we prove several results concerning universality and homogeneity of the space $$\kappa ^\kappa $$ , with $$\kappa $$ a regular uncountable cardinal, using generalized ultrametrics.- 16 January 2025
- Published by Springer Nature in Results in Mathematics
- Vol. 80 (1) , 1-23
Open AccessOn Generic Topological Embeddings
We show that an embedding of a fixed 0-dimensional compact space K into the Čech–Stone remainder $$\omega ^*$$ as a nowhere dense P-set is the unique generic limit, a special object in the category consisting of all continuous maps from K to compact metric spaces. Using categorical Fraïssé theory, we obtain some well-known theorems about Čech–Stone remainders of infinite discrete spaces. Furthermore, we prove several results concerning universality and homogeneity of the space $$\kappa ^\kappa $$ , with $$\kappa $$ a regular uncountable cardinal, using generalized ultrametrics. - 25 April 2023
- Published by Elsevier in Topology and its Applications
- Vol. 334
Scattered P-spaces of weight ω1
- 25 April 2023
- Published by Elsevier in Topology and its Applications
- Vol. 334
Scattered P-spaces of weight ω1
- 7 March 2022
- Published by Elsevier in Topology and its Applications
- Vol. 312, 108064
Inverse limits which are P-spaces
- 7 March 2022
- Published by Elsevier in Topology and its Applications
- Vol. 312, 108064
Inverse limits which are P-spaces
- 1 January 2021
- Published by Institute of Mathematics, Czech Academy of Sciences in Mathematica Bohemica
- Vol. 146 (4) , 457-469
THE NIEMYTZKI PLANE IS x-METRIZABLE
We prove that the Niemytzki plane is x-metrizable and we try to explain the differences between the concepts of a stratifiable space and a x-metrizable space. Also, we give a characterisation of x-metrizable spaces which is modelled on the version described by Chigogidze.
- 1 January 2021
- Published by Institute of Mathematics, Czech Academy of Sciences in Mathematica Bohemica
- Vol. 146 (4) , 457-469
THE NIEMYTZKI PLANE IS x-METRIZABLE
We prove that the Niemytzki plane is x-metrizable and we try to explain the differences between the concepts of a stratifiable space and a x-metrizable space. Also, we give a characterisation of x-metrizable spaces which is modelled on the version described by Chigogidze.
- 23 May 2020
- Published by Walter de Gruyter GmbH in Mathematica Slovaca
- Vol. 70 (3) , 775-777
An internal characterization of complete regularity
This note presents a short proof of an internal characterization of complete regularity.
- 23 May 2020
- Published by Walter de Gruyter GmbH in Mathematica Slovaca
- Vol. 70 (3) , 775-777
An internal characterization of complete regularity
This note presents a short proof of an internal characterization of complete regularity.
- 1 December 2019
- Published by Elsevier in Topology and its Applications
- Vol. 268
A generalization of ϰ-metrizable spaces
- 1 December 2019
- Published by Elsevier in Topology and its Applications
- Vol. 268
A generalization of ϰ-metrizable spaces
- Open Access
The Niemytzki plane is kappa-metrizable
We try to explain the differences between the concepts of stratifiable space and $\varkappa$-metrizable space. In particular, we give a characterization of $\varkappa$-metrizable spaces which is modelled on Chigogidze's characterization. Moreover, we present a $\varkappa$-metric for the Niemytzki plane, using the properties of the Euclidean metric.
Open AccessThe Niemytzki plane is kappa-metrizable
We try to explain the differences between the concepts of stratifiable space and $\varkappa$-metrizable space. In particular, we give a characterization of $\varkappa$-metrizable spaces which is modelled on Chigogidze's characterization. Moreover, we present a $\varkappa$-metric for the Niemytzki plane, using the properties of the Euclidean metric.
- Open Access
- 18 July 2019
- Published by Walter de Gruyter GmbH in Annales Mathematicae Silesianae
- Vol. 33 (1) , 41-54
Topological Spaces with the Freese–Nation Property
We give a proposal of generalization of the Freese–Nation property for topological spaces. We introduce a few properties related to Freese–Nation property: FNS, FN, FNS*, FNI. This article presents some relationship between these concepts. We show that spaces with the FNS property satisfy ccc and any product of such spaces also satisfies ccc. We show that all metrizable spaces have the FN property.
- 18 July 2019
- Published by Walter de Gruyter GmbH in Annales Mathematicae Silesianae
- Vol. 33 (1) , 41-54
Open AccessTopological Spaces with the Freese–Nation Property
We give a proposal of generalization of the Freese–Nation property for topological spaces. We introduce a few properties related to Freese–Nation property: FNS, FN, FNS*, FNI. This article presents some relationship between these concepts. We show that spaces with the FNS property satisfy ccc and any product of such spaces also satisfies ccc. We show that all metrizable spaces have the FN property.
- Open Access
- 10 July 2019
- Published by Springer Nature in Archiv der Mathematik
- Vol. 114 (1) , 51-59
The Banach–Mazur game and domain theory
- 10 July 2019
- Published by Springer Nature in Archiv der Mathematik
- Vol. 114 (1) , 51-59
Open AccessThe Banach–Mazur game and domain theory