Ideals of nowhere dense sets in some topologies on positive integers

Marta Kwela , Andrzej Nowik

Abstract

We investigate the ideals of nowhere dense sets in three topologies on N (namely, the Furstenberg's, Golomb's, and Kirch's topology) related to arithmetic progressions. In particular, we explore relationships between these ideals, and show that each of them has a topological representation and cannot be extended to a summable ideal. Moreover, we study a related notion of Marczewski-Burstin countable representability.
Author Marta Kwela (FMPI / IM)
Marta Kwela,,
- Institute of Mathematics
, Andrzej Nowik (FMPI / IM)
Andrzej Nowik,,
- Institute of Mathematics
Journal seriesTopology and Its Applications, ISSN 0166-8641, (A 20 pkt)
Issue year2018
Vol248
Pages149-163
Publication size in sheets0.7
Keywords in Englishideals, Furstenberg’s topology, Golomb’s topology, Kirch’s topology, Marczewski-Burstin representability
ASJC Classification2608 Geometry and Topology
DOIDOI:10.1016/j.topol.2018.08.015
URL https://doi.org/10.1016/j.topol.2018.08.015
Languageen angielski
Score (nominal)20
ScoreMinisterial score = 20.0, 24-07-2019, ArticleFromJournal
Publication indicators WoS Citations = 0; Scopus SNIP (Source Normalised Impact per Paper): 2017 = 1.051; WoS Impact Factor: 2017 = 0.549 (2) - 2017=0.579 (5)
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