Pseudometric spaces: From minimality to maximality in the groups of combinatorial self-similarities
The group of combinatorial self-similarities of a pseudometric space (X,d)\left(X,d) is the maximal subgroup of the symmetric group Sym(X){\rm{Sym}}\left(X) whose elements preserve the four-point equality d(x,y)=d(u,v)d\left(x,y)=d\left(u,v). Let us denote by ℐP{\mathcal{ {\mathcal I} P}} the class...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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De Gruyter
2023-12-01
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| Series: | Analysis and Geometry in Metric Spaces |
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| Online Access: | https://doi.org/10.1515/agms-2023-0103 |
| _version_ | 1797316662137978880 |
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| author | Bilet Viktoriia Dovgoshey Oleksiy |
| author_facet | Bilet Viktoriia Dovgoshey Oleksiy |
| author_sort | Bilet Viktoriia |
| collection | DOAJ |
| description | The group of combinatorial self-similarities of a pseudometric space (X,d)\left(X,d) is the maximal subgroup of the symmetric group Sym(X){\rm{Sym}}\left(X) whose elements preserve the four-point equality d(x,y)=d(u,v)d\left(x,y)=d\left(u,v). Let us denote by ℐP{\mathcal{ {\mathcal I} P}} the class of all pseudometric spaces (X,d)\left(X,d) for which every combinatorial self-similarity Φ:X→X\Phi :X\to X satisfies the equality d(x,Φ(x))=0,d\left(x,\Phi \left(x))=0, but all permutations of metric reflection of (X,d)\left(X,d) are combinatorial self-similarities of this reflection. The structure of ℐP{\mathcal{ {\mathcal I} P}}-spaces is fully described. |
| first_indexed | 2024-03-08T03:21:40Z |
| format | Article |
| id | doaj.art-684e371770e94dd0aedf2f391de36964 |
| institution | Directory Open Access Journal |
| issn | 2299-3274 |
| language | English |
| last_indexed | 2024-03-08T03:21:40Z |
| publishDate | 2023-12-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Analysis and Geometry in Metric Spaces |
| spelling | doaj.art-684e371770e94dd0aedf2f391de369642024-02-12T09:11:32ZengDe GruyterAnalysis and Geometry in Metric Spaces2299-32742023-12-0111173374610.1515/agms-2023-0103Pseudometric spaces: From minimality to maximality in the groups of combinatorial self-similaritiesBilet Viktoriia0Dovgoshey Oleksiy1Department of Theory of Functions Institute of Applied Mathematics and Mechanics of NASU, Dobrovolskogo str. 1, Slovyansk, 84100, UkraineDepartment of Theory of Functions Institute of Applied Mathematics and Mechanics of NASU, Dobrovolskogo str. 1, Slovyansk, 84100, UkraineThe group of combinatorial self-similarities of a pseudometric space (X,d)\left(X,d) is the maximal subgroup of the symmetric group Sym(X){\rm{Sym}}\left(X) whose elements preserve the four-point equality d(x,y)=d(u,v)d\left(x,y)=d\left(u,v). Let us denote by ℐP{\mathcal{ {\mathcal I} P}} the class of all pseudometric spaces (X,d)\left(X,d) for which every combinatorial self-similarity Φ:X→X\Phi :X\to X satisfies the equality d(x,Φ(x))=0,d\left(x,\Phi \left(x))=0, but all permutations of metric reflection of (X,d)\left(X,d) are combinatorial self-similarities of this reflection. The structure of ℐP{\mathcal{ {\mathcal I} P}}-spaces is fully described.https://doi.org/10.1515/agms-2023-0103combinatorial similaritydiscrete pseudometricequivalence relationstrongly rigid pseudometricsymmetric groupprimary 54e35secondary 20m05 |
| spellingShingle | Bilet Viktoriia Dovgoshey Oleksiy Pseudometric spaces: From minimality to maximality in the groups of combinatorial self-similarities Analysis and Geometry in Metric Spaces combinatorial similarity discrete pseudometric equivalence relation strongly rigid pseudometric symmetric group primary 54e35 secondary 20m05 |
| title | Pseudometric spaces: From minimality to maximality in the groups of combinatorial self-similarities |
| title_full | Pseudometric spaces: From minimality to maximality in the groups of combinatorial self-similarities |
| title_fullStr | Pseudometric spaces: From minimality to maximality in the groups of combinatorial self-similarities |
| title_full_unstemmed | Pseudometric spaces: From minimality to maximality in the groups of combinatorial self-similarities |
| title_short | Pseudometric spaces: From minimality to maximality in the groups of combinatorial self-similarities |
| title_sort | pseudometric spaces from minimality to maximality in the groups of combinatorial self similarities |
| topic | combinatorial similarity discrete pseudometric equivalence relation strongly rigid pseudometric symmetric group primary 54e35 secondary 20m05 |
| url | https://doi.org/10.1515/agms-2023-0103 |
| work_keys_str_mv | AT biletviktoriia pseudometricspacesfromminimalitytomaximalityinthegroupsofcombinatorialselfsimilarities AT dovgosheyoleksiy pseudometricspacesfromminimalitytomaximalityinthegroupsofcombinatorialselfsimilarities |