Molica Bisci, Giovanni; Repovš, Dušan D.; Zdomskyy, Lyubomyr Coideals as remainders of groups distinguishing between combinatorial covering properties. (English) Zbl 07781613 Topology Appl. 340, Article ID 108725, 15 p. (2023). Summary: In this paper we construct consistent examples of subgroups of \(2^\omega\) with Menger remainders which fail to have other stronger combinatorial covering properties. This answers several open questions asked by Bella, Tokgoz and Zdomskyy (Arch. Math. Logic 55 (2016), 767-784). MSC: 03E75 Applications of set theory 54D40 Remainders in general topology 54D20 Noncompact covering properties (paracompact, Lindelöf, etc.) 03E35 Consistency and independence results 54D80 Special constructions of topological spaces (spaces of ultrafilters, etc.) Keywords:remainder; topological group; Menger space; Scheepers space; filter; forcing × Cite Format Result Cite Review PDF Full Text: DOI arXiv References: [1] Arhangel’skii, A., Two types of remainders of topological groups. Comment. Math. Univ. Carol., 119-126 (2008) · Zbl 1212.54086 [2] Arhangel’skii, A., The Baire property in remainders of topological groups and other results. Comment. Math. Univ. Carol., 273-279 (2009) · Zbl 1212.54098 [3] Arhangel’skii, A.; Choban, M., Properties of remainders of topological groups and of their perfect images. Topol. Appl. (2021), 8 pp. · Zbl 1469.54006 [4] Arhangel’skii, A.; van Mill, J., On topological groups with a first-countable remainder. Topol. Proc., 157-163 (2013) · Zbl 1285.54027 [5] Arhangel’skii, A.; van Mill, J., On topological groups with a first-countable remainder, III. Indag. Math. (N. S.), 35-43 (2014) · Zbl 1295.54034 [6] Arhangel’skii, A.; van Mill, J., On topological groups with a first-countable remainder, II. Topol. Appl., 143-150 (2015) · Zbl 1331.54041 [7] Babinkostova, L.; Kočinac, L. D.R.; Scheepers, M., Combinatorics of open covers (VIII). Topol. Appl., 15-32 (2004) · Zbl 1051.54019 [8] Bella, A.; Tokgoz, S.; Zdomskyy, L., Menger remainders of topological groups. Arch. Math. Log., 767-784 (2016) · Zbl 1370.03075 [9] Blass, A., Combinatorial cardinal characteristics of the continuum, 395-491 · Zbl 1198.03058 [10] Blass, A.; Laflamme, C., Consistency results about filters and the number of inequivalent growth types. J. Symb. Log., 50-56 (1989) · Zbl 0673.03038 [11] Blass, A.; Shelah, S., Near coherence of filters. III. A simplified consistency proof. Notre Dame J. Form. Log., 530-538 (1989) · Zbl 0702.03030 [12] Chodounský, D.; Repovš, D.; Zdomskyy, L., Mathias forcing and combinatorial covering properties of filters. J. Symb. Log., 1398-1410 (2015) · Zbl 1350.54019 [13] Engelking, R., General Topology. Monografie Matematyczne (1977), PWN—Polish Scientific Publishers: PWN—Polish Scientific Publishers Warsaw · Zbl 0373.54002 [14] Guzmán, O.; Hrušák, M.; Martínez, A. A., Canjar filters. Notre Dame J. Form. Log., 79-95 (2017) · Zbl 1417.03247 [15] Guzmán, O.; Hrušák, M.; Martínez, A. A., Canjar filters II: Proofs of \(\mathfrak{b} < \mathfrak{s}\) and \(\mathfrak{b} < \mathfrak{a}\) revisited, 59-67 [16] Henriksen, M.; Isbell, J. R., Some properties of compactifications. Duke Math. J., 83-105 (1957) · Zbl 0081.38604 [17] Hrušák, M., Combinatorics of Filters and Ideals, 29-69 · Zbl 1239.03030 [18] Hurewicz, W., Über die Verallgemeinerung des Borellschen Theorems. Math. Z., 401-421 (1925) · JFM 51.0454.02 [19] Hurewicz, W., Über Folgen stetiger Funktionen. Fundam. Math., 193-204 (1927) · JFM 53.0562.03 [20] Just, W.; Miller, A. W.; Scheepers, M.; Szeptycki, P. J., The combinatorics of open covers. II. Topol. Appl., 241-266 (1996) · Zbl 0870.03021 [21] Krupski, M., Games and hereditary Baireness in hyperspaces and spaces of probability measures. J. Inst. Math. Jussieu, 3, 851-868 (2022) · Zbl 1498.54016 [22] Laflamme, C., Forcing with filters and complete combinatorics. Ann. Pure Appl. Log., 125-163 (1989) · Zbl 0681.03035 [23] Marciszewski, M., P-filters and hereditary Baire function spaces. Topol. Appl., 241-247 (1998) · Zbl 0969.54016 [24] Medini, A.; Zdomskyy, L., Every filter is homeomorphic to its square. Bull. Pol. Acad. Sci., Math., 63-67 (2016) · Zbl 1391.03035 [25] Repovš, D.; Zdomskyy, L.; Zhang, S., Countable dense homogeneous filters and the Menger covering property. Fundam. Math., 233-240 (2014) · Zbl 1344.54002 [26] Scheepers, M., Combinatorics of open covers. I. Ramsey theory. Topol. Appl., 31-62 (1996) · Zbl 0848.54018 [27] Shelah, S., Proper and Improper Forcing. Perspectives in Mathematical Logic (1998), Springer-Verlag: Springer-Verlag Berlin · Zbl 0889.03041 [28] Zdomskyy, L., A semifilter approach to selection principles. Comment. Math. Univ. Carol., 525-539 (2005) · Zbl 1121.03060 [29] Zdomskyy, L., Products of Menger spaces in the Miller model. Adv. Math., 170-179 (2018) · Zbl 1522.03222 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.