Pub Date : 2024-01-12DOI: 10.30970/vmm.2022.94.056-071
M. Cencelj, Oleg Gutik, Duvsan D. Repovvs
We show that every Hausdorff Baire topology $tau$ on $mathcal{C}=langle a,bmid a^2b=a, ab^2=brangle$ such that $(mathcal{C},tau)$ is a semitopological semigroup is discrete and we construct a nondiscrete Hausdorff semigroup topology on $mathcal{C}$. We also discuss the closure of a semigroup $mathcal{C}$ in a semitopological semigroup and prove that $mathcal{C}$ does not embed into a topological semigroup with the countably compact square.
{"title":"On some generalization of the bicyclic semigroup: the topological version","authors":"M. Cencelj, Oleg Gutik, Duvsan D. Repovvs","doi":"10.30970/vmm.2022.94.056-071","DOIUrl":"https://doi.org/10.30970/vmm.2022.94.056-071","url":null,"abstract":"We show that every Hausdorff Baire topology $tau$ on $mathcal{C}=langle a,bmid a^2b=a, ab^2=brangle$ such that $(mathcal{C},tau)$ is a semitopological semigroup is discrete and we construct a nondiscrete Hausdorff semigroup topology on $mathcal{C}$. We also discuss the closure of a semigroup $mathcal{C}$ in a semitopological semigroup and prove that $mathcal{C}$ does not embed into a topological semigroup with the countably compact square.","PeriodicalId":277870,"journal":{"name":"Visnyk Lvivskogo Universytetu Seriya Mekhaniko-Matematychna","volume":"58 23","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139532877","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-05-13DOI: 10.30970/vmm.2022.93.005-013
I. Banakh, T. Banakh, Maria Kolinko, A. Ravsky
A subset $X$ of an Abelian group $G$ is called $semiaf!fine$ if for every $x,y,zin X$ the set ${x+y-z,x-y+z}$ intersects $X$. We prove that a subset $X$ of an Abelian group $G$ is semiaffine if and only if one of the following conditions holds: (1) $X=(H+a)cup (H+b)$ for some subgroup $H$ of $G$ and some elements $a,bin X$; (2) $X=(Hsetminus C)+g$ for some $gin G$, some subgroup $H$ of $G$ and some midconvex subset $C$ of the group $H$. A subset $C$ of a group $H$ is $midconvex$ if for every $x,yin C$, the set $frac{x+y}2:={zin H:2z=x+y}$ is a subset of $C$.
{"title":"Semiaffine sets in Abelian groups","authors":"I. Banakh, T. Banakh, Maria Kolinko, A. Ravsky","doi":"10.30970/vmm.2022.93.005-013","DOIUrl":"https://doi.org/10.30970/vmm.2022.93.005-013","url":null,"abstract":"A subset $X$ of an Abelian group $G$ is called $semiaf!fine$ if for every $x,y,zin X$ the set ${x+y-z,x-y+z}$ intersects $X$. We prove that a subset $X$ of an Abelian group $G$ is semiaffine if and only if one of the following conditions holds: (1) $X=(H+a)cup (H+b)$ for some subgroup $H$ of $G$ and some elements $a,bin X$; (2) $X=(Hsetminus C)+g$ for some $gin G$, some subgroup $H$ of $G$ and some midconvex subset $C$ of the group $H$. A subset $C$ of a group $H$ is $midconvex$ if for every $x,yin C$, the set $frac{x+y}2:={zin H:2z=x+y}$ is a subset of $C$.","PeriodicalId":277870,"journal":{"name":"Visnyk Lvivskogo Universytetu Seriya Mekhaniko-Matematychna","volume":"2020 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114821234","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-02-16DOI: 10.30970/vmm.2021.91.040-053
O. Gutik
We study feebly compact shift-continuous $T_1$-topologies on the symmetric inverse semigroup $mathscr{I}_lambda^n$ of finite transformations of the rank $leqslant n$. It is proved that such $T_1$-topology is sequentially pracompact if and only if it is feebly compact. Also, we show that every shift-continuous feebly $omega$-bounded $T_1$-topology on $mathscr{I}_lambda^n$ is compact.
{"title":"A note on feebly compact semitopological symmetric inverse semigroups of a bounded finite rank","authors":"O. Gutik","doi":"10.30970/vmm.2021.91.040-053","DOIUrl":"https://doi.org/10.30970/vmm.2021.91.040-053","url":null,"abstract":"We study feebly compact shift-continuous $T_1$-topologies on the symmetric inverse semigroup $mathscr{I}_lambda^n$ of finite transformations of the rank $leqslant n$. It is proved that such $T_1$-topology is sequentially pracompact if and only if it is feebly compact. Also, we show that every shift-continuous feebly $omega$-bounded $T_1$-topology on $mathscr{I}_lambda^n$ is compact.","PeriodicalId":277870,"journal":{"name":"Visnyk Lvivskogo Universytetu Seriya Mekhaniko-Matematychna","volume":"43 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-02-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124002461","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-01-31DOI: 10.30970/vmm.2021.92.005-016
O. Gutik, Oksana Prokhorenkova, D. Sekh
It is proved that the semigroups $mathrm{mathbf{End}}(boldsymbol{B}_{omega})$ and $mathrm{mathbf{End}}(boldsymbol{B}_{mathbb{Z}})$ of the endomorphisms of the bicyclic semigroup $boldsymbol{B}_{omega}$ and the endomorphisms of the extended bicyclic semigroup $boldsymbol{B}_{mathbb{Z}}$ are isomorphic to the semidirect products $(omega,+)rtimes_varphi(omega,*)$ and $mathbb{Z}(+)rtimes_varphi(omega,*)$, respectively.
{"title":"On endomorphisms of the bicyclic semigroup and the extended bicyclic semigroup","authors":"O. Gutik, Oksana Prokhorenkova, D. Sekh","doi":"10.30970/vmm.2021.92.005-016","DOIUrl":"https://doi.org/10.30970/vmm.2021.92.005-016","url":null,"abstract":"It is proved that the semigroups $mathrm{mathbf{End}}(boldsymbol{B}_{omega})$ and $mathrm{mathbf{End}}(boldsymbol{B}_{mathbb{Z}})$ of the endomorphisms of the bicyclic semigroup $boldsymbol{B}_{omega}$ and the endomorphisms of the extended bicyclic semigroup $boldsymbol{B}_{mathbb{Z}}$ are isomorphic to the semidirect products $(omega,+)rtimes_varphi(omega,*)$ and $mathbb{Z}(+)rtimes_varphi(omega,*)$, respectively.","PeriodicalId":277870,"journal":{"name":"Visnyk Lvivskogo Universytetu Seriya Mekhaniko-Matematychna","volume":"62 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128857414","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1900-01-01DOI: 10.30970/vmm.2021.91.054-062
M. Zabolotskyi, Yuriy Gal, Mariana Mostova
{"title":"Logarithmic derevative and angular density of zeros for the Blaschke product","authors":"M. Zabolotskyi, Yuriy Gal, Mariana Mostova","doi":"10.30970/vmm.2021.91.054-062","DOIUrl":"https://doi.org/10.30970/vmm.2021.91.054-062","url":null,"abstract":"","PeriodicalId":277870,"journal":{"name":"Visnyk Lvivskogo Universytetu Seriya Mekhaniko-Matematychna","volume":"94 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127068971","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1900-01-01DOI: 10.30970/vmm.2021.91.005-027
Oleg Gutik, M. Mykhalenych
{"title":"ON GROUP CONGRUENCES ON THE SEMIGROUP BFomega AND ITS HOMOMORPHIC RETRACTS IN THE CASE WHEN THE FAMILY F CONSISTS OF INDUCTIVE NON-EMPTY SUBSETS OF omega","authors":"Oleg Gutik, M. Mykhalenych","doi":"10.30970/vmm.2021.91.005-027","DOIUrl":"https://doi.org/10.30970/vmm.2021.91.005-027","url":null,"abstract":"","PeriodicalId":277870,"journal":{"name":"Visnyk Lvivskogo Universytetu Seriya Mekhaniko-Matematychna","volume":"29 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121328619","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1900-01-01DOI: 10.30970/vmm.2021.92.034-050
Oleg Gutik, Oleksandra Lysetska
{"title":"On the semigroup BFomega which is generated by the family F of atomic subsets of omega","authors":"Oleg Gutik, Oleksandra Lysetska","doi":"10.30970/vmm.2021.92.034-050","DOIUrl":"https://doi.org/10.30970/vmm.2021.92.034-050","url":null,"abstract":"","PeriodicalId":277870,"journal":{"name":"Visnyk Lvivskogo Universytetu Seriya Mekhaniko-Matematychna","volume":"89 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121679064","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1900-01-01DOI: 10.30970/vmm.2022.93.122
Taras Banakh, Oleg Gutik, Yaroslav Prytula
{"title":"The common meeting of the Mathematical Commission of the Taras Shevchenko Scientific Society, Lviv Mathematical Society and Polish Mathematical Society","authors":"Taras Banakh, Oleg Gutik, Yaroslav Prytula","doi":"10.30970/vmm.2022.93.122","DOIUrl":"https://doi.org/10.30970/vmm.2022.93.122","url":null,"abstract":"","PeriodicalId":277870,"journal":{"name":"Visnyk Lvivskogo Universytetu Seriya Mekhaniko-Matematychna","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122856535","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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