All Questions
7
questions
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\...
- 977
2
votes
0
answers
191
views
A question about infinite product of Baire and meager spaces
Proposition 1: For any space $X$ and an infinite cardinal $\kappa$, the product $X^{\kappa}$ is either meager or a Baire space.
Does anyone have any suggestions to demonstrate Proposition 1?
I was ...
- 551
5
votes
0
answers
167
views
Can maximal filters of nowhere meager subsets of Cantor space be countably complete?
Let $X$ denote Cantor space. A subset $A\subseteq X$ is nowhere meager if for every non-empty open $U\subseteq X$, we have $A\cap U$ non-meager. We call $\mathcal{F}\subseteq \mathcal{P}(X)$ a maximal ...
- 369
1
vote
1
answer
237
views
Borel hierarchy and tail sets
Let $A$ be a finite set, and let $A^\infty$ be the set of all sequences $(a_n)_{n=1}^\infty$ of elements of $A$.
A set $B \subseteq A^\infty$ is a tail set if for every two sequences $\vec a, \vec b \...
- 705
3
votes
0
answers
208
views
Nowhere Baire spaces
Studying the article "Barely Baire spaces" of W. Fleissner and K. Kunen, using stationary sets, they show an example of a Baire space whose square is nowhere Baire (we call a space $X$ nowhere Baire ...
- 551
10
votes
0
answers
485
views
Is there a model of set theory in which $\mathfrak p< \mathfrak b < \mathfrak q$?
Is there a model of set theory in which $\mathfrak p< \mathfrak b < \mathfrak q$?
Here $\mathfrak p$, $\mathfrak b$, $\mathfrak q$ are small uncountable cardinals:
$\mathfrak p$ is the ...
- 977
3
votes
4
answers
636
views
Picking a real for every non-empty open set in $\mathbb{R}$
Let ${\cal E}$ denote the collection of open sets of $\mathbb{R}$ with respect to the Euclidean topology. It is well known that $|{\cal E}| = 2^{\aleph_0}$. Is there an injective map $f:{\cal E}\...
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