All Questions
Tagged with independence-results gn.general-topology
11 questions
3
votes
1
answer
125
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Perfectly normal but not collectionwise normal space in ZFC
In the article A Perfectly Normal, Locally Compact, Noncollectionwise Normal Space Form $\lozenge^\ast$ by Daniels and Gruenhage (I presume "form" is a typo and it should be "from",...
- 5,596
3
votes
0
answers
79
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Is $\mathfrak q_0$ equal to the smallest cardinality of a second-countable $T_1$-space which is not a $Q$-space?
A topological space $X$ is a $Q$-space if every subset of $X$ is of type $G_\delta$.
The smallest cardinality of a metrizable separable space which is not a $Q$-space is denoted by $\mathfrak q_0$ and ...
- 41.8k
4
votes
1
answer
194
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Is every first-countable Lindelof space of cardinality $<\mathfrak c$ a $Q$-space under MA?
Definition. A topological space $X$ is a $Q$-space if every subset of $X$ is of type $G_\delta$.
It is clear that every $Q$-space has countable pseudocharacter (= all singletons are $G_\delta$) and is ...
- 674
5
votes
1
answer
197
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The cardinal characteristic $\mathfrak r_{(X,f)}$ of a dynamical system
I am interested in a "dynamical" modification of the cardinals $\mathfrak r$ and $\mathfrak r_\sigma$, well-known in the theory of cardinal characteristics of the continuum.
For a compact ...
- 41.8k
4
votes
1
answer
396
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Is there a universally meager air space?
Let $\mathcal P$ be a family of nonempty subsets of a topological space $X$. A subset $D\subset X$ is called $\mathcal P$-generic if for any $P\in\mathcal P$ the intersection $P\cap D$ is not empty.
A ...
- 41.8k
1
vote
0
answers
289
views
About Whitehead's problem
Hi I am new to proofs of consistency and independence with ZFC of some claims. I have read "The uses of set theory" by Judith Roitman, in that article it is mentioned that the Whitehead ...
- 561
33
votes
1
answer
2k
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Is it still an open problem whether $\mathbb{R}^\omega$ is normal in the box topology?
On page 205 of his Topology textbook, James Munkres made an interesting remark:
It is not known whether $\mathbb{R}^\omega$ is normal in the box topology. Mary-Ellen Rudin has shown that the answer ...
- 18.5k
5
votes
1
answer
524
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A topologically transitive dynamical system without dense orbits
By a dynamical system I understand a pair $(K,G)$ consisting a compact Hausdorff space and a subgroup $G$ of the homeomorphism group of $K$.
We say that a dynamical system $(K,G)$
$\bullet$ is ...
- 41.8k
32
votes
1
answer
2k
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Bidi: A new cardinal characteristic of the continuum?
This question assumes familiarity with combinatorial cardinal
characteristics of the continuum.
Identify an infinite set $a\subseteq\mathbb{N}$ with its increasing
enumeration. Thus, for each natural ...
- 4,713
2
votes
0
answers
120
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Two small uncountable cardinals related to Q-sets
A subset $A$ of the real line is called a Q-set if any subset of of $A$ is of type $F_\sigma$ in $A$.
Let $\mathfrak q_0$ be the smallest cardinality of a subset $X\subset\mathbb R$ which is not a Q-...
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4
votes
1
answer
223
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K-analytic spaces whose any compact subset is countable
A regular topological space $X$ is called
$\bullet$ analytic if $X$ is a continuous image of a Polish space;
$\bullet$ $K$-analytic if $X$ is the image of a Polish space $P$ under an upper ...
- 41.8k