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Results tagged with selection-principles
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user 61536
2
votes
A selection principle in measure theory
Professor Wladyslaw Wilczynski kindly informed me that the answer to this problem is negative.
Take any Lebesgue null dense $G_\delta$-set $A$ in the real line $\mathbb R$. Choose a countable dense su …
- 42k
5
votes
Accepted
Are σ-sets preserved by Borel isomorphisms?
Under some set-theoretic assumptions the answer to this question is negative.
Namely, if there exists a $Q$-set $X$, then $X$ is a $\sigma$-set which is Borel isomorphic to a (hereditarily normal co …
- 42k
13
votes
Accepted
A ridiculous combinatorial cardinal characteristic of the continuum?
The cardinal $\mathfrak{ridiculous}$ is equal to $\mathfrak p$ (which is equal to the smallest character of a free filter without infinite pseudointesection on $\omega$). It suffices to prove that a f …
- 42k
9
votes
Is there a condensation from $\aleph_1^{\aleph_0}$ onto a metrizable compact space?
The answer is affirmative and can be derived from
Theorem (Banakh, Plichko). The Hilbert space $\ell_2(\aleph_1)$ condenses onto the Hilbert cube.
By the way, this theorem is related to Problem 1 f …
- 42k