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Results tagged with selection-principles
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user 5903
3
votes
Does there exist a strongly star-Lindelöf space which is not DCCC?
Every strongly star-Lindelöf $T_1$-space is DCCC.
Let $\mathcal{U}$ be a discrete family of non-empty open sets in the space $X$, and pick a point $x_U\in U$ for each $U\in\mathcal{U}$.
The set $F=\{x …
- 11.4k
4
votes
Does there exist a star-Lindelöf space which is not DCCC?
There is no $T_1$-example: assume $X$ is $T_1$ and star-Lindelöf. Let $\mathcal{D}$ be a discrete family of open sets.
Choose $x_D\in D$ for all $D\in\mathcal{D}$ and put $A=\{x_D:D\in\mathcal{D}\}$.
…
- 11.4k
5
votes
Accepted
Is there a metric separable space with the following properties...?
Let $X$ be a Bernstein subset of $\mathbb{R}$, so $X$ and its complement intersect every uncountable closed set in $\mathbb{R}$.
Let $f:X\to\mathbb{R}$ be continuous and assume $f[X]$ is uncountable. …
- 11.4k
9
votes
Accepted
Is it true that $\mathit{MA}(\omega_1)$ iff $\omega_1<\mathfrak{p}$?
Q1: No, see Between Martin's Axiom and Souslin's Hypothesis by Kunen and Tall. Note: Bell proved in The combinatorial principle $P(\mathfrak{c})$ that $\mathfrak{p}>\aleph_1$ is equivalent to $\mathsf …
- 11.4k