Abstract
We show that PFA implies that the tightness t(Xδ) of the Gδ-modification of a Fréchet α1-space X is at most ω1, while (κ) implies that there is a Fréchet α1-space with Gδ-tightness equal to κ. We use the example constructed from (κ) to show that a local version of the bound t(Xδ) ≤ 2t(X)L(X) does not hold. We also construct, assuming MA, an example of a Fréchet space whose Gδ-tightness is larger than ω1.
Original language | English |
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Pages (from-to) | 195-202 |
Number of pages | 8 |
Journal | Fundamenta Mathematicae |
Volume | 251 |
Issue number | 2 |
DOIs | |
State | Published - 1 Jan 2020 |
Externally published | Yes |
Keywords
- Fréchet-Urysohn
- G-modification
- PFA
- Square principles
- Tightness
- α1-spaces
ASJC Scopus subject areas
- Algebra and Number Theory