Iranian Mathematical SocietyJournal of the Iranian Mathematical Society2717-16123220220701Asymptotically equicontinuous sequences of operators and a Banach--Steinhaus type theorem434715879310.30504/jims.2022.361848.1073ENJ.MashreghiDépartement de mathématiques et de statistique, Université
Laval, Québec City (Québec), G1V 0A6, Canada.T.RansfordDépartement de mathématiques et de statistique, Université
Laval, Québec City (Québec), G1V 0A6, Canada.Journal Article20220912We introduce the notion of an asymptotically equicontinuous sequence of linear operators, and use it to prove the following result. If $X,Y$ are topological vector spaces, if $T_n,T:X\to Y$ are continuous linear maps, and if $D$ is a dense subset of $X$, then the following statements are equivalent: $(i) ~T_nx\to Tx$ for all $x\in X$, and $(ii) ~T_n x\to Tx$ for all $x\in D$ and the sequence $(T_n)$ is asymptotically equicontinuous.https://jims.ims.ir/article_158793_c943ab0912cd39cc1ced48d8fc141d1e.pdfIranian Mathematical SocietyJournal of the Iranian Mathematical Society2717-16123220220701Minimal generating sequences of F-subgroups496016359110.30504/jims.2022.367761.1079ENA.LucchiniDepartment of Mathematics, Tullio Levi Civita, University of Padova, Italy.0000-0002-2134-4991Journal Article20221030The behaviour of generating sets of finite groups has been widely studied, from several points of view. The purpose of this note is to investigate what happens when, instead of sets of elements generating a group, sets of subgroups belonging to a prescribed family are considered. Some known results on generating set can be extended and generalized, using similar arguments and techniques, but interesting open questions also arise.https://jims.ims.ir/article_163591_21ec2d6d025874bef0fc3edac90be261.pdfIranian Mathematical SocietyJournal of the Iranian Mathematical Society2717-16123220220701Bohr conditions and almost periodic means in quasi-complete spaces617316482310.30504/jims.2023.366124.1077ENY.ZhuDepartment of Mathematics, University of Windsor, Ontario, Canada.M.Sangani MonfaredDepartment of Mathematics, University of Windsor, Ontario, Canada.Journal Article20221017We study Bohr conditions for functions on topological groups taking values in locally convex spaces. We show that functions satisfying Bohr conditions are uniformly continuous. We show that in quasi-complete spaces, Bohr conditions are equivalent to Bochner's characterizations of almost periodicity. We prove the existence of invariant mean for almost periodic functions with values in quasi-complete spaces.https://jims.ims.ir/article_164823_9887bae3f051b9f09befe3a9a4992769.pdfIranian Mathematical SocietyJournal of the Iranian Mathematical Society2717-16123220220701A topologist's interactions with Derek J. S. Robinson and his mathematics759016971010.30504/jims.2023.379086.1082ENM.TimmDepartment of Mathematics, Bradley University Peoria, IL 61625, U.S.A.Journal Article20230102The paper begins with a brief history of this topologist's interactions with Derek J. S. Robinson. It continues with a topological proof of Derek's result showing that the Schur multiplier of a generalized Baumslag-Solitar group $G$ is free abelian of rank one less than the rank of the torsion free first homology of $G$ and that both of these ranks can be computed by inspecting a weighted directed graph associate to $G$. In this paper the topology of a special subclass of Seifert fibred 2-dimensional complexes is used to provide proofs of Derek's results.https://jims.ims.ir/article_169710_cd0884e80cd6dbf501625a1d27b9c7ef.pdf