Article
| Title: | Special sets of reals and weak forms of normality on Isbell--Mrówka spaces (English) |
| Author: | de Oliveira Rodrigues, Vinicius |
| Author: | dos Santos Ronchim, Victor |
| Author: | Szeptycki, Paul J. |
| Language: | English |
| Journal: | Commentationes Mathematicae Universitatis Carolinae |
| ISSN: | 0010-2628 (print) |
| ISSN: | 1213-7243 (online) |
| Volume: | 64 |
| Issue: | 1 |
| Year: | 2023 |
| Pages: | 109-126 |
| Summary lang: | English |
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| Category: | math |
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| Summary: | We recall some classical results relating normality and some natural weakenings of normality in $\Psi$-spaces over almost disjoint families of branches in the Cantor tree to special sets of reals like $Q$-sets, $\lambda$-sets and $\sigma$-sets. We introduce a new class of special sets of reals which corresponds to the corresponding almost disjoint family of branches being $\aleph_0$-separated. This new class fits between $\lambda$-sets and perfectly meager sets. We also discuss conditions for an almost disjoint family $\mathcal A$ being potentially almost-normal (pseudonormal), in the sense that $\mathcal A$ is almost-normal (pseudonormal) in some c.c.c. forcing extension. (English) |
| Keyword: | Isbell--Mrówka spaces |
| Keyword: | almost disjoint families |
| Keyword: | almost-normal |
| Keyword: | weak $\lambda$-set |
| MSC: | 54D15 |
| MSC: | 54D80 |
| idZBL: | Zbl 07790586 |
| idMR: | MR4631794 |
| DOI: | 10.14712/1213-7243.2023.014 |
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| Date available: | 2023-08-28T09:51:02Z |
| Last updated: | 2024-02-13 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/151804 |
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