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Relating the cut distance and the weak* topology for graphons

The result's identifiers

  • Result code in IS VaVaI

    <a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985807%3A_____%2F21%3A00536782" target="_blank" >RIV/67985807:_____/21:00536782 - isvavai.cz</a>

  • Alternative codes found

    RIV/67985840:_____/21:00536782

  • Result on the web

    <a href="https://doi.org/10.1016/j.jctb.2020.04.003" target="_blank" >https://doi.org/10.1016/j.jctb.2020.04.003</a>

  • DOI - Digital Object Identifier

    <a href="http://dx.doi.org/10.1016/j.jctb.2020.04.003" target="_blank" >10.1016/j.jctb.2020.04.003</a>

Alternative languages

  • Result language

    angličtina

  • Original language name

    Relating the cut distance and the weak* topology for graphons

  • Original language description

    The theory of graphons is ultimately connected with the so-called cut norm. In this paper, we approach the cut norm topology via the weak* topology (when considering a predual of L1-functions). We prove that a sequence W1, W2, W3, ... of graphons converges in the cut distance if and only if we have equality of the sets of weak* accumulation points and of weak* limit points of all sequences of graphons W1, W2, W3, ... that are weakly isomorphic to W1, W2, W3, ... . We further give a short descriptive set theoretic argument that each sequence of graphons contains a subsequence with the property above. This in particular provides an alternative proof of the theorem of Lovász and Szegedy about compactness of the space of graphons. We connect these results to 'multiway cut' characterization of cut distance convergence from [Ann. of Math. (2) 176 (2012), no. 1, 151-219]. These results are more naturally phrased in the Vietoris hyperspace K over graphons with the weak* topology.

  • Czech name

  • Czech description

Classification

  • Type

    J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database

  • CEP classification

  • OECD FORD branch

    10101 - Pure mathematics

Result continuities

  • Project

    Result was created during the realization of more than one project. More information in the Projects tab.

  • Continuities

    I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Others

  • Publication year

    2021

  • Confidentiality

    S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Data specific for result type

  • Name of the periodical

    Journal of Combinatorial Theory. B

  • ISSN

    0095-8956

  • e-ISSN

    1096-0902

  • Volume of the periodical

    147

  • Issue of the periodical within the volume

    March

  • Country of publishing house

    US - UNITED STATES

  • Number of pages

    47

  • Pages from-to

    252-298

  • UT code for WoS article

    000605462900011

  • EID of the result in the Scopus database

    2-s2.0-85084518436