Ideal QN-spaces
Autor: | Jaroslav Šupina |
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Rok vydání: | 2016 |
Předmět: |
Discrete mathematics
Ideal (set theory) Mathematics::Commutative Algebra Applied Mathematics 010102 general mathematics Ideal norm Minimal ideal Baire space 01 natural sciences 010101 applied mathematics Primary ideal Principal ideal Radical of an ideal Maximal ideal 0101 mathematics Analysis Mathematics |
Zdroj: | Journal of Mathematical Analysis and Applications. 435:477-491 |
ISSN: | 0022-247X |
Popis: | We continue to investigate an ideal version of QN-space, a JQN-space, introduced by P. Das and D. Chandra [8]. Following R. Filipow and M. Staniszewski [15], we show that an ideal J on ω contains an isomorphic copy of the ideal Fin×Fin on ω×ω if and only if every topological space is a JQN-space. If J does not contain an isomorphic copy of the ideal Fin×Fin then the Baire space ωω is not a JQN-space. However, if p=c then there is an ideal J not containing an isomorphic copy of the ideal Fin×Fin and there is a JQN-space which is not a QN-space. We prove few results related to an ideal version of an S1(Γ,Γ)-space. Indeed, we show that there is no ideal J such that the notion of an S1(Γ,J-Γ)-space is trivial. Consequently the ideal version of Scheepers' Conjecture does not hold for ideals containing an isomorphic copy of Fin×Fin. |
Databáze: | OpenAIRE |
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