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On the homotopy sets of simply connected rational CW-complexes 单连通有理cw -复形的同伦集
IF 0.6 3区 数学
Acta Mathematica Hungarica Pub Date : 2025-09-22 DOI: 10.1007/s10474-025-01554-y
M. Benkhalifa
{"title":"On the homotopy sets of simply connected rational CW-complexes","authors":"M. Benkhalifa","doi":"10.1007/s10474-025-01554-y","DOIUrl":"10.1007/s10474-025-01554-y","url":null,"abstract":"<div><p>Let <i>X</i> and <i>Y</i> be two simply connected rational CW-complexes, and <span>(n in mathbb{N})</span>. We study the homotopy set <span>([P^nX, P^nY])</span>, where <i>P</i><sup><i>n</i></sup><i>X</i> and <i>P</i><sup><i>n</i></sup><i>Y</i> are the <span>(n)</span>-th Postnikov sections of <i>X</i> and <i>Y</i>, respectively. An equivalence relation is defined on this set, revealing connections with the cohomology groups. This approach uses rational homotopy theory to uncover new structural insights.</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"176 2","pages":"522 - 531"},"PeriodicalIF":0.6,"publicationDate":"2025-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10474-025-01554-y.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145230450","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Clustering in typical unit-distance avoiding sets 典型单位距离回避集的聚类
IF 0.6 3区 数学
Acta Mathematica Hungarica Pub Date : 2025-09-22 DOI: 10.1007/s10474-025-01556-w
A. Cohen, N. Mani
{"title":"Clustering in typical unit-distance avoiding sets","authors":"A. Cohen,&nbsp;N. Mani","doi":"10.1007/s10474-025-01556-w","DOIUrl":"10.1007/s10474-025-01556-w","url":null,"abstract":"<div><p>In the 1960s Moser asked how dense a subset of <span>(mathbb{R}^d)</span> can be if no pairs of points in the subset are exactly distance 1 apart.\u0000There has been a long line of work showing upper bounds on this density. One curious feature of dense unit distance avoiding sets is that they appear to be ''clumpy,'' i.e. forbidding unit distances comes hand in hand with having more than the expected number distance <span>(approx 2)</span> pairs. </p><p>In this work we rigorously establish this phenomenon in <span>(mathbb{R}^2)</span>. We show that dense unit distance avoiding sets have over-represented distance <span>(approx 2)</span> pairs, and that this clustering extends to typical unit distance avoiding sets. To do so, we build off of the linear programming approach used previously to prove upper bounds on the density of unit distance avoiding sets.</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"176 2","pages":"473 - 497"},"PeriodicalIF":0.6,"publicationDate":"2025-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145230448","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Measure theoretic equicontinuity and sensitivity via Furstenberg family 通过Furstenberg族测量理论的等连续性和灵敏度
IF 0.6 3区 数学
Acta Mathematica Hungarica Pub Date : 2025-09-22 DOI: 10.1007/s10474-025-01558-8
H. Ju, Y. Ju, J. Kim
{"title":"Measure theoretic equicontinuity and sensitivity via Furstenberg family","authors":"H. Ju,&nbsp;Y. Ju,&nbsp;J. Kim","doi":"10.1007/s10474-025-01558-8","DOIUrl":"10.1007/s10474-025-01558-8","url":null,"abstract":"<div><p>We consider measure theoretic equicontinuity and sensitivity via Furstenberg family. We introduce the notion of <span>(mathcal {F})</span>-<span>(mu)</span>-equicontinuity which is the refined version of <span>(mu )</span>-equicontinuity using Furstenberg family <span>(mathcal {F})</span> and prove that when <span>(mathcal {F})</span> is a filter, a given dynamical system <span>((X,T))</span> is <span>(mathcal {F})</span>-<span>(mu)</span>-equicontinuous if and only if it is <span>(mathcal {F})</span>-<span>(mu)</span>-<span>(f)</span>-equicontinuous with respect to every continuous function <span>(f colon {X to mathbb {C}} )</span>. In addition, under certain conditinos, we prove that an ergodic measure theoretic dynamical system is either <span>(kmathcal {F})</span>-<span>(mu )</span>-sensitive or <span>(mathcal {F})</span>-<span>(mu)</span>-equicontinuous.</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"176 2","pages":"291 - 312"},"PeriodicalIF":0.6,"publicationDate":"2025-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145230395","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Problems in additive number theory. VI: Sizes of sumsets of finite sets 加性数论中的若干问题。有限集合的集合的大小
IF 0.6 3区 数学
Acta Mathematica Hungarica Pub Date : 2025-09-22 DOI: 10.1007/s10474-025-01559-7
M. B. Nathanson
{"title":"Problems in additive number theory. VI: Sizes of sumsets of finite sets","authors":"M. B. Nathanson","doi":"10.1007/s10474-025-01559-7","DOIUrl":"10.1007/s10474-025-01559-7","url":null,"abstract":"<div><p>In the study of sums of finite sets of integers, most attention has been paid to sets with small sumsets (Freiman's theorem and related work) and to sets with large sumsets (Sidon sets and <span>(B_h)</span>-sets). This paper focuses on the full range of sizes of <span>(h)</span>-fold sums of a set of <span>(k)</span> integers. Many new results and open problems are presented.</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"176 2","pages":"498 - 521"},"PeriodicalIF":0.6,"publicationDate":"2025-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145230393","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On (F)-spaces of almost-Lebesgue functions 关于近似勒贝格函数的(F) -空间
IF 0.6 3区 数学
Acta Mathematica Hungarica Pub Date : 2025-09-22 DOI: 10.1007/s10474-025-01552-0
N. J. Alves
{"title":"On (F)-spaces of almost-Lebesgue functions","authors":"N. J. Alves","doi":"10.1007/s10474-025-01552-0","DOIUrl":"10.1007/s10474-025-01552-0","url":null,"abstract":"<div><p>We consider the space of functions almost in <span>(L_p)</span> and endow it with the topology of asymptotic <span>(L_p)</span>-convergence. This yields a completely metrizable topological vector space which, on finite measure spaces, coincides with the space of measurable functions equipped with the topology of (local) convergence in measure. We investigate analogs of classical results such as dominated convergence and Vitali convergence theorems. For <span>(mathbb{R}^d)</span> as the underlying measure space, we establish results on approximation by smooth functions and separability. Further aspects, including local boundedness, local convexity, and duality are examined in the <span>(mathbb{R}^d)</span> setting, revealing fundamental differences from standard <span>(L_p)</span> spaces.</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"176 2","pages":"365 - 386"},"PeriodicalIF":0.6,"publicationDate":"2025-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10474-025-01552-0.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145230394","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On open-separated sequences 关于开分隔序列
IF 0.6 3区 数学
Acta Mathematica Hungarica Pub Date : 2025-09-22 DOI: 10.1007/s10474-025-01553-z
A. Bella, N. Carlson, S. Spadaro, P. Szeptycki
{"title":"On open-separated sequences","authors":"A. Bella,&nbsp;N. Carlson,&nbsp;S. Spadaro,&nbsp;P. Szeptycki","doi":"10.1007/s10474-025-01553-z","DOIUrl":"10.1007/s10474-025-01553-z","url":null,"abstract":"<div><p>\u0000We introduce the notion of an open-separated sequence, related to a free sequence, and define the cardinal function\u0000<span>(text{os} ( X))</span>. Nonregular and regular examples <span>(X)</span> are given such that <span>(text{os} ( X)&lt;F(X))</span>. Motivated by a question of Angelo Bella, we show that if\u0000<span>(X)</span> is Hausdorff then <span>(|X|leq hL(X)^{text{os} ( X)psi_c(X)})</span>. As\u0000<span>(text{os} ( X)psi_c(X)leq hL(X))</span> if <span>(X)</span> is Hausdorff, this gives a\u0000strengthening of the De Groot-Smirnov bound <span>(2^{hL(X)})</span> for the\u0000cardinality of a Hausdorff space. Additionally we show <span>( text{nw}( X)leq text{hL}(X)^{text {os} ( X)})</span> if <span>(X)</span> is regular. A consequence is that if <span>(X)</span> is regular and either almost radial or hereditarily weakly Whyburn then <span>( { |X|leq hL(X)^{text{os} ( X)} } )</span>.\u0000</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"176 2","pages":"387 - 399"},"PeriodicalIF":0.6,"publicationDate":"2025-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10474-025-01553-z.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145230396","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Rotational beta expansions and Schmidt games 旋转beta扩展和施密特游戏
IF 0.6 3区 数学
Acta Mathematica Hungarica Pub Date : 2025-09-22 DOI: 10.1007/s10474-025-01555-x
J. Caalim, H. Kaneko, N. Nollen
{"title":"Rotational beta expansions and Schmidt games","authors":"J. Caalim,&nbsp;H. Kaneko,&nbsp;N. Nollen","doi":"10.1007/s10474-025-01555-x","DOIUrl":"10.1007/s10474-025-01555-x","url":null,"abstract":"<div><p>\u0000We consider rotational beta expansions in dimensions 1, 2 and 4 and view them as expansions on real numbers, complex numbers, and quaternions, respectively.\u0000We give sufficient conditions on the parameters <span>(alpha, beta in (0,1))</span> so that particular cylinder sets arising from the expansions are winning or losing Schmidt <span>((alpha,beta))</span>-game.\u0000</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"176 2","pages":"400 - 436"},"PeriodicalIF":0.6,"publicationDate":"2025-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145230451","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Olsen's inequality for discrete Morrey spaces 离散Morrey空间的Olsen不等式
IF 0.6 3区 数学
Acta Mathematica Hungarica Pub Date : 2025-09-22 DOI: 10.1007/s10474-025-01557-9
H. Gunawan, Y. Ramadana, Y. Sawano
{"title":"Olsen's inequality for discrete Morrey spaces","authors":"H. Gunawan,&nbsp;Y. Ramadana,&nbsp;Y. Sawano","doi":"10.1007/s10474-025-01557-9","DOIUrl":"10.1007/s10474-025-01557-9","url":null,"abstract":"<div><p>\u0000The aim of this paper is to establish the Olsen's inequality for discrete Morrey spaces. Specifically, it focuses on a bilinear operator associated with the discrete fractional integral operator of order <span>(alpha)</span> within these spaces. To achieve this, the decomposition method for discrete Morrey spaces is thoroughly examined.\u0000</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"176 2","pages":"447 - 456"},"PeriodicalIF":0.6,"publicationDate":"2025-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145230414","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On some hereditary and super classes of directly finite Abelian groups 直接有限阿贝尔群的一些遗传和超类
IF 0.6 3区 数学
Acta Mathematica Hungarica Pub Date : 2025-08-26 DOI: 10.1007/s10474-025-01546-y
P. Danchev, B. Goldsmith, F. Karimi
{"title":"On some hereditary and super classes of directly finite Abelian groups","authors":"P. Danchev,&nbsp;B. Goldsmith,&nbsp;F. Karimi","doi":"10.1007/s10474-025-01546-y","DOIUrl":"10.1007/s10474-025-01546-y","url":null,"abstract":"<div><p>Continuing recent studies of both the hereditary and super properties of certain classes of Abelian groups, we explore in-depth what is the situation in the quite large class consisting of directly finite Abelian groups.</p><p>Trying to connect some of these classes, we specifically succeeded to prove the surprising criteria that a relatively Hopfian group is hereditarily Hopfian only when it is extended Bassian, as well as that, a relatively Hopfian group is super Hopfian only when it is extended Bassian. In this aspect, additional relevant necessary and sufficient conditions in a slightly more general context are also proved.</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"176 2","pages":"457 - 472"},"PeriodicalIF":0.6,"publicationDate":"2025-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10474-025-01546-y.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145230235","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
An approximation form of the Kuratowski Extension Theorem for Baire-alpha functions 函数的Kuratowski扩展定理的近似形式
IF 0.6 3区 数学
Acta Mathematica Hungarica Pub Date : 2025-07-29 DOI: 10.1007/s10474-025-01550-2
W. Sieg
{"title":"An approximation form of the Kuratowski Extension Theorem for Baire-alpha functions","authors":"W. Sieg","doi":"10.1007/s10474-025-01550-2","DOIUrl":"10.1007/s10474-025-01550-2","url":null,"abstract":"<div><p>Let <span>(Omega)</span> be a perfectly normal topological space, let <span>(A)</span> be a non-empty <span>(G_delta)</span>-subset of <span>(Omega)</span> and let <span>(mathscr{B}_1(A))</span> denote the space of all functions <span>(Atomathbb {R})</span> of Baire-one class on <span>(A)</span>.\u0000Let also <span>(|cdot|_infty)</span> be the supremum norm. The symbol <span>(chi_A)</span> stands for the characteristic function of <span>(A)</span>. We prove that for every bounded function <span>(finmathscr {B}_1(A))</span> there is a sequence <span>((H_n))</span>\u0000of both <span>(F_sigma)</span>- and <span>(G_delta)</span>-subset of <span>(Omega)</span> such that the function <span>(overline{f}colonOmegatomathbb {R})</span> given by the uniformly convergent series on <span>(Omega)</span> with the formula:\u0000<span>( overline{f}:=csum_{n=0}^infty (frac{2}{3})^{n+1}(frac{1}{2}-chi_{H_n}) )</span>\u0000extends <span>(f)</span> with <span>(overline{f}in{mathscr{B}}_1(Omega))</span>, <span>(c=sup_{xinOmega}lvert{overline{f}(x)}rvert)</span> and the condition <span>((triangle))</span> of the form:\u0000<span>(|f|_infty=|overline{f}|_infty)</span>.\u0000We apply the above series to obtain an extension of <span>(f)</span> positive to <span>(overline{f})</span> positive with the condition <span>((triangle))</span>. A similar technique allows us to obtain an extension of Baire-alpha function\u0000on <span>(A)</span> to Baire-alpha function on <span>(Omega)</span>.\u0000</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"176 2","pages":"313 - 320"},"PeriodicalIF":0.6,"publicationDate":"2025-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10474-025-01550-2.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145230333","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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