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seen Jan 1 at 13:15

Jan
1
comment Does countable intersection of linear subspaces with finite codimensions have countable codimension?
Thanks for your example.
Jan
1
answered The weak$^*$ topology on $X^*$ is not first countable if $X$ has uncountable dimension.
Jan
1
comment The weak$^*$ topology on $X^*$ is not first countable if $X$ has uncountable dimension.
Thank you very much. I think the last comment by @DavidMitra is the answer. Do you want to write up the answer? Or should I answer my own question?
Jan
1
comment The weak$^*$ topology on $X^*$ is not first countable if $X$ has uncountable dimension.
But Uniform Boundedness Theorem requires the normed space in question to be complete, right?
Jan
1
comment The weak$^*$ topology on $X^*$ is not first countable if $X$ has uncountable dimension.
Thank you. But why are weak* convergent sequences norm-bounded?
Dec
31
comment The weak$^*$ topology on $X^*$ is not first countable if $X$ has uncountable dimension.
You mean this sequence in $X^*$? I see where this is going. The sequence is w*-bounded, but not norm-bounded. This is not quite a contradiction because w*-boundedness and norm-boundedness are not quite the same.
Dec
31
asked The weak$^*$ topology on $X^*$ is not first countable if $X$ has uncountable dimension.
Dec
31
answered Does countable intersection of linear subspaces with finite codimensions have countable codimension?
Dec
31
awarded  Commentator
Dec
31
comment Does countable intersection of linear subspaces with finite codimensions have countable codimension?
Thanks. So maybe take $F_n=\{f: f(q_n)=0\}$ where $\{q_n:n\in \mathbb{N}\}=\mathbb{Q}\cap [0,1]$?
Dec
31
comment Does countable intersection of linear subspaces with finite codimensions have countable codimension?
@Amr the codimension of subspace $W$ in a vector space $V$ is the dimension of $V/W$.
Dec
31
comment Does countable intersection of linear subspaces with finite codimensions have countable codimension?
@hardmath Which way are we going? To show it true or to show it false?
Dec
31
comment Does countable intersection of linear subspaces with finite codimensions have countable codimension?
Do you mean $V_n=F_1\cap F_2\cap \dots \cap F_n$?
Dec
31
asked Does countable intersection of linear subspaces with finite codimensions have countable codimension?
Feb
11
awarded  Supporter
Feb
8
answered Given $\int_0^1 x f(x)dx=0$, show that $\int_0^1|1-f(x)|dx>1/2$
Oct
21
accepted Let $\alpha$ be a root of $X^3+X^2-2X+1\in\mathbb{Q}[X]$.
Oct
21
comment Let $\alpha$ be a root of $X^3+X^2-2X+1\in\mathbb{Q}[X]$.
Just in case you might think I have typed the question wrong, I did not. I have triple checked.
Oct
21
asked Let $\alpha$ be a root of $X^3+X^2-2X+1\in\mathbb{Q}[X]$.
Oct
20
awarded  Teacher