Pub Date : 2023-04-28DOI: 10.14712/1213-7243.2023.009
Masoumeh Sajjadi
{"title":"On the recognizability of some projective general linear groups by the prime graph","authors":"Masoumeh Sajjadi","doi":"10.14712/1213-7243.2023.009","DOIUrl":"https://doi.org/10.14712/1213-7243.2023.009","url":null,"abstract":"","PeriodicalId":44396,"journal":{"name":"Commentationes Mathematicae Universitatis Carolinae","volume":" ","pages":""},"PeriodicalIF":0.2,"publicationDate":"2023-04-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44157800","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 : 2023-04-28DOI: 10.14712/1213-7243.2023.011
Sergei Logunov
{"title":"On Szymański theorem on hereditary normality of $betaomega$","authors":"Sergei Logunov","doi":"10.14712/1213-7243.2023.011","DOIUrl":"https://doi.org/10.14712/1213-7243.2023.011","url":null,"abstract":"","PeriodicalId":44396,"journal":{"name":"Commentationes Mathematicae Universitatis Carolinae","volume":" ","pages":""},"PeriodicalIF":0.2,"publicationDate":"2023-04-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46820369","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 : 2023-04-28DOI: 10.14712/1213-7243.2023.002
Kamal El Fahri, H. Khabaoui, J. H’michane
{"title":"On the class of order almost L-weakly compact operators","authors":"Kamal El Fahri, H. Khabaoui, J. H’michane","doi":"10.14712/1213-7243.2023.002","DOIUrl":"https://doi.org/10.14712/1213-7243.2023.002","url":null,"abstract":"","PeriodicalId":44396,"journal":{"name":"Commentationes Mathematicae Universitatis Carolinae","volume":" ","pages":""},"PeriodicalIF":0.2,"publicationDate":"2023-04-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49398659","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 : 2023-04-28DOI: 10.14712/1213-7243.2023.010
Marianne Morillon
. We show that in set-theory without the axiom of choice ZF , the statement sH : (cid:16)Every proper closed subset of a (cid:28)nitary matroid is the intersection of hyperplanes including it(cid:17) implies AC fin , the axiom of choice for (nonempty) (cid:28)nite sets. We also provide an equivalent of the statement AC fin in terms of (cid:16)graphic(cid:17) matroids. Several open questions stay open in ZF , for example: does sH imply the Axiom of Choice?
{"title":"Hyperplanes in matroids and the axiom of choice","authors":"Marianne Morillon","doi":"10.14712/1213-7243.2023.010","DOIUrl":"https://doi.org/10.14712/1213-7243.2023.010","url":null,"abstract":". We show that in set-theory without the axiom of choice ZF , the statement sH : (cid:16)Every proper closed subset of a (cid:28)nitary matroid is the intersection of hyperplanes including it(cid:17) implies AC fin , the axiom of choice for (nonempty) (cid:28)nite sets. We also provide an equivalent of the statement AC fin in terms of (cid:16)graphic(cid:17) matroids. Several open questions stay open in ZF , for example: does sH imply the Axiom of Choice?","PeriodicalId":44396,"journal":{"name":"Commentationes Mathematicae Universitatis Carolinae","volume":" ","pages":""},"PeriodicalIF":0.2,"publicationDate":"2023-04-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43133617","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 : 2023-02-14DOI: 10.14712/1213-7243.2022.021
V. Tkachuk
{"title":"Exponential separability is preserved by some products","authors":"V. Tkachuk","doi":"10.14712/1213-7243.2022.021","DOIUrl":"https://doi.org/10.14712/1213-7243.2022.021","url":null,"abstract":"","PeriodicalId":44396,"journal":{"name":"Commentationes Mathematicae Universitatis Carolinae","volume":" ","pages":""},"PeriodicalIF":0.2,"publicationDate":"2023-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49397287","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 : 2023-02-13DOI: 10.14712/1213-7243.2022.022
José del Carmen Alberto-Domínguez, G. Acosta, M. Madriz-Mendoza
{"title":"The common division topology on $mathbb{N}$","authors":"José del Carmen Alberto-Domínguez, G. Acosta, M. Madriz-Mendoza","doi":"10.14712/1213-7243.2022.022","DOIUrl":"https://doi.org/10.14712/1213-7243.2022.022","url":null,"abstract":"","PeriodicalId":44396,"journal":{"name":"Commentationes Mathematicae Universitatis Carolinae","volume":" ","pages":""},"PeriodicalIF":0.2,"publicationDate":"2023-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48971072","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 : 2023-02-13DOI: 10.14712/1213-7243.2022.027
Alan Murat
{"title":"Mersenne numbers as a difference of two Lucas numbers","authors":"Alan Murat","doi":"10.14712/1213-7243.2022.027","DOIUrl":"https://doi.org/10.14712/1213-7243.2022.027","url":null,"abstract":"","PeriodicalId":44396,"journal":{"name":"Commentationes Mathematicae Universitatis Carolinae","volume":" ","pages":""},"PeriodicalIF":0.2,"publicationDate":"2023-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42683621","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 : 2023-02-13DOI: 10.14712/1213-7243.2023.003
Claude Tardif
We prove that for any c ≥ 5, there exists an infinite family (Gn)n∈N of graphs such that χ(Gn) > c for all n ∈ N and χ(Gm×Gn) ≤ c for all m 6= n. These counterexamples to Hedetniemi’s conjecture show that the Boolean lattices of exponential graphs with Kc as a base are infinite for c ≥ 5.
我们证明了对于任意c≥5，存在一个图的无限族（Gn）n∈n，使得所有n∈n的χ（Gn。
{"title":"Counterexamples to Hedetniemi's conjecture and infinite Boolean lattices","authors":"Claude Tardif","doi":"10.14712/1213-7243.2023.003","DOIUrl":"https://doi.org/10.14712/1213-7243.2023.003","url":null,"abstract":"We prove that for any c ≥ 5, there exists an infinite family (Gn)n∈N of graphs such that χ(Gn) > c for all n ∈ N and χ(Gm×Gn) ≤ c for all m 6= n. These counterexamples to Hedetniemi’s conjecture show that the Boolean lattices of exponential graphs with Kc as a base are infinite for c ≥ 5.","PeriodicalId":44396,"journal":{"name":"Commentationes Mathematicae Universitatis Carolinae","volume":" ","pages":""},"PeriodicalIF":0.2,"publicationDate":"2023-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43403612","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 : 2023-02-13DOI: 10.14712/1213-7243.2022.024
A. Hager, Brian Wynne
{"title":"The category of compactifications and its coreflections","authors":"A. Hager, Brian Wynne","doi":"10.14712/1213-7243.2022.024","DOIUrl":"https://doi.org/10.14712/1213-7243.2022.024","url":null,"abstract":"","PeriodicalId":44396,"journal":{"name":"Commentationes Mathematicae Universitatis Carolinae","volume":" ","pages":""},"PeriodicalIF":0.2,"publicationDate":"2023-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42245755","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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