All Questions
7
questions
3
votes
0
answers
140
views
Which cardinal $\kappa\geq \omega_1$ is critical for the following property...?
Which cardinal $\kappa\geq \omega_1$ is critical for the following property:
Let $X\subset \mathbb R$ and $\kappa>|X|\geq \omega_1$. Then there is an uncountable family $\{X_{\alpha}\}$ such that $...
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2
votes
0
answers
151
views
Is there a Lusin space $X$ such that ...?
Is there a Lusin space (in the sense Kunen) $X$ such that
$X$ is Tychonoff;
$X$ is a $\gamma$-space ?
Note that if $X$ is metrizable and a $\gamma$-space then it is not Lusin.
In mathematics, a ...
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4
votes
1
answer
283
views
Almost compact sets
Update:
Q1 is answered in the comments.
I think that the usual arguments show that every relatively almost compact set in a space is closed in the space.
Original question:
A set $K$ in a space $X$ ...
- 2,978
5
votes
1
answer
363
views
Is it true that $\mathit{MA}(\omega_1)$ iff $\omega_1<\mathfrak{p}$?
Recall that
$\mathfrak{p}=\min\{|F|: F$ is a subfamily of $[\omega]^{\omega}$ with the sfip which has no infinite pseudo-intersection $\}$.
The cardinal $\mathfrak{q}_0$ defined as the smallest ...
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3
votes
1
answer
87
views
Is there a hereditary $\sigma$-space $X$ such that it is not $Q$-space?
A topological space $X$ is called a $\sigma$-space if every $F_{\sigma}$-subset of $X$ is $G_{\delta}$.
A topological space $X$ is called a $Q$-space if any subset of $X$ is $F_{\sigma}$.
Definition. ...
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4
votes
0
answers
123
views
An uncountable Baire γ-space without an isolated point exists?
An open cover $U$ of a space $X$ is:
• an $\omega$-cover if $X$ does not belong to $U$ and every finite subset of $X$ is contained in a member of $U$.
• a $\gamma$-cover if it is infinite and each $x\...
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7
votes
1
answer
202
views
Are σ-sets preserved by Borel isomorphisms?
Recall that a $\sigma$-space is a topological space such that every $F_{\sigma}$-set is $G_{\delta}$-set.
$X$ - $\sigma$-set, if $X$ is a $\sigma$-space and it is subset of real line $R$.
Let $F$ ...
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