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Gabriel Medina's user avatar
Gabriel Medina
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A question about infinite product of Baire and meager spaces
My question for the proof the before lemma is : Why BCT implies that there is a non-empty open Baire subset $U$ of $X^{\kappa}$?
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A question about infinite product of Baire and meager spaces
Lemma 4.2 in the article : A countable dense homogeneous topological vector space is a Baire space (doi.org/10.1090/proc/15271).
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A question about infinite product of Baire and meager spaces
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A question about infinite product of Baire and meager spaces
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A question about infinite product of Baire and meager spaces
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A question about infinite product of Baire and meager spaces
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Topological spaces that resemble the space of irrationals
@Noah Schweber Thanks a lot.
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Products of Baire spaces
Yes, thanks a lot.
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Products of Baire spaces
Thanks for the remark, how about now?
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Products of Baire spaces
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Products of Baire spaces
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Products of Baire spaces
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Question about additive subgroups of the real line and the density topology
Hi @Slup, I modified some things from my last answer. Did you study White's example? If so, I wanted to tell you something about it. In case you are interested, you can write me a message to the email [email protected]
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Question about additive subgroups of the real line and the density topology
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Question about additive subgroups of the real line and the density topology
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Question about additive subgroups of the real line and the density topology
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CH and the density topology on $\mathbb{R}$
Thanks a lot @KP Hart. Only two remarks, the first we need that $0<c<1$, this is possible because $c=m^{*}(Y\cap ]0,1[)<1$. The second, as $A\in\mathcal{T}\setminus \{\emptyset\}$, then $m(A)>0$, so I think that this is the contradiction.
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CH and the density topology on $\mathbb{R}$
Thanks a lot @KP Hart. Now it's much clearer to me. Do you have any reference, for the fact that if a set $Y$ is closed under shifting and scaling by rational numbers.then there is a constant $c$ such that $m^{*}(Y\cap (a,b)) = c⋅(b−a)$ for every interval $(a,b)$?
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