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
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Czech description
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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