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• W2757307890 abstract "This paper is devoted to studies of IwQN-spaces and some of their cardinal characteristics. Recently, v{S}upina proved that I is not a weak P-ideal if and only if any topological space is an IQN-space. Moreover, under $mathfrak{p}=mathfrak{c}$ he constructed a maximal ideal I (which is not a weak P-ideal) for which the notions of IQN-space and QN-space do not coincide. In this paper we show that, consistently, there is an ideal I (which is not a weak P-ideal) for which the notions of IwQN-space and wQN-space do not coincide. We also prove that for this ideal the ideal version of Scheepers Conjecture does not hold (this is the first known example of such weak P-ideal). We obtain a strictly combinatorial characterization of ${tt non}(text{IwQN-space})$ similar to the one given by v{S}upina in the case of ${tt non}(text{IQN-space})$. We calculate ${tt non}(text{IQN-space})$ and ${tt non}(text{IwQN-space})$ for some weak P-ideals. Namely, we show that $mathfrak{b}leq{tt non}(text{IQN-space})leq{tt non}(text{IwQN-space})leqmathfrak{d}$ for every weak P-ideal I and that ${tt non}(text{IQN-space})={tt non}(text{IwQN-space})=mathfrak{b}$ for every $mathtt{F_sigma}$ ideal I as well as for every analytic P-ideal I generated by an unbounded submeasure (this establishes some new bounds for $mathfrak{b}(I,I,Fin)$). As a consequence, we obtain some bounds for ${tt add}(text{IQN-space})$. In particular, we get ${tt add}(text{IQN-space})=mathfrak{b}$ for analytic P-ideals I generated by an unbounded submeasure. By a result of Bukovsk'y, Das and v{S}upina it is known that in the case of tall ideals I the notions of IQN-space (IwQN-space) and QN-space (wQN-space) cannot be distinguished. We prove that if I is a tall ideal and X is a topological space of cardinality less than ${tt cov^*}(I)$, then X is an IwQN-space if and only if it is a wQN-space." @default.
• W2757307890 created "2017-10-06" @default.
• W2757307890 creator A5052726386 @default.
• W2757307890 date "2018-05-01" @default.
• W2757307890 modified "2023-10-18" @default.
• W2757307890 title "Ideal weak QN-spaces" @default.
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• W2757307890 doi "https://doi.org/10.1016/j.topol.2018.03.007" @default.
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