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- Title
Special subsets of the generalized Cantor space and generalized Baire space.
- Authors
Korch, Michał; Weiss, Tomasz
- Abstract
In this paper, we are interested in parallels to the classical notions of special subsets in R defined in the generalized Cantor and Baire spaces (2κ and κκ). We consider generalizations of the well‐known classes of special subsets, like Lusin sets, strongly null sets, concentrated sets, perfectly meagre sets, σ‐sets, γ‐sets, sets with the Menger, the Rothberger, or the Hurewicz property, but also of some less‐know classes like X‐small sets, meagre additive sets, Ramsey null sets, Marczewski, Silver, Miller, and Laver‐null sets. We notice that many classical theorems regarding these classes can be relatively easy generalized to higher cardinals although sometimes with some additional assumptions. This paper serves as a catalogue of such results along with some other generalizations and open problems.
- Subjects
BAIRE spaces; GENERALIZED spaces; RAMSEY theory; GENERALIZATION; CARDINAL numbers; CANTOR sets
- Publication
Mathematical Logic Quarterly, 2020, Vol 66, Issue 4, p418
- ISSN
0942-5616
- Publication type
Article
- DOI
10.1002/malq.201800004