Asymptotic structures of cardinals
A ballean is a set X endowed with some family F of its subsets, called the balls, in such a way that (X,F) can be considered as an asymptotic counterpart of a uniform topological space. Given a cardinal k, we define F using a natural order structure on k. We characterize balleans up to coarse equiv...
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Universitat Politècnica de València
2014-07-01
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| Series: | Applied General Topology |
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| Online Access: | http://polipapers.upv.es/index.php/AGT/article/view/3109 |
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doaj-f8ff4d4da73e4a62ba698827d3ac67a22020-11-24T21:35:36ZengUniversitat Politècnica de ValènciaApplied General Topology1576-94021989-41472014-07-0115213714610.4995/agt.2014.31092618Asymptotic structures of cardinalsOleksandr Petrenko0Igor V. Protasov1Sergii Slobodianiuk2Kyiv National UniversityKyiv UniversityKyiv National UniversityA ballean is a set X endowed with some family F of its subsets, called the balls, in such a way that (X,F) can be considered as an asymptotic counterpart of a uniform topological space. Given a cardinal k, we define F using a natural order structure on k. We characterize balleans up to coarse equivalence, give the criterions of metrizability and cellularity, calculate the basic cardinal invariant of these balleans. We conclude the paper with discussion of some special ultrafilters on cardinal balleans.http://polipapers.upv.es/index.php/AGT/article/view/3109cardinal balleanscoarse equivalencemetrizabilitycellularitycardinal invariantsultrafilter. |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Oleksandr Petrenko Igor V. Protasov Sergii Slobodianiuk |
| spellingShingle |
Oleksandr Petrenko Igor V. Protasov Sergii Slobodianiuk Asymptotic structures of cardinals Applied General Topology cardinal balleans coarse equivalence metrizability cellularity cardinal invariants ultrafilter. |
| author_facet |
Oleksandr Petrenko Igor V. Protasov Sergii Slobodianiuk |
| author_sort |
Oleksandr Petrenko |
| title |
Asymptotic structures of cardinals |
| title_short |
Asymptotic structures of cardinals |
| title_full |
Asymptotic structures of cardinals |
| title_fullStr |
Asymptotic structures of cardinals |
| title_full_unstemmed |
Asymptotic structures of cardinals |
| title_sort |
asymptotic structures of cardinals |
| publisher |
Universitat Politècnica de València |
| series |
Applied General Topology |
| issn |
1576-9402 1989-4147 |
| publishDate |
2014-07-01 |
| description |
A ballean is a set X endowed with some family F of its subsets, called the balls, in such a way that (X,F) can be considered as an asymptotic counterpart of a uniform topological space. Given a cardinal k, we define F using a natural order structure on k. We characterize balleans up to coarse equivalence, give the criterions of metrizability and cellularity, calculate the basic cardinal invariant of these balleans. We conclude the paper with discussion of some special ultrafilters on cardinal balleans. |
| topic |
cardinal balleans coarse equivalence metrizability cellularity cardinal invariants ultrafilter. |
| url |
http://polipapers.upv.es/index.php/AGT/article/view/3109 |
| work_keys_str_mv |
AT oleksandrpetrenko asymptoticstructuresofcardinals AT igorvprotasov asymptoticstructuresofcardinals AT sergiislobodianiuk asymptoticstructuresofcardinals |
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1725944984247468032 |