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Jan
4
comment Help to understand a proof (about filters)
@KarlKronenfeld: I am lost. Don't we suppose that $\bigcap K$ is not the cofinite filter? But $A'\in G$ would follow from $\bigcap K$ being a cofinite filter.
Jan
3
comment Help to understand a proof (about filters)
I also do not understand the overall proof: groups.google.com/d/msg/sci.math/NMTPqI8h13I/2U-qetLK_MgJ - pleas help.
Jan
3
comment Help to understand a proof (about filters)
@NielsDiepeveen: Why $A'\in G$ for some $G\in K$?
Jan
2
comment Help to understand a proof (about filters)
But how to prove that $\bigcap K$ being cofinite implies for every infinite $A$ there exists $G\in K$ with $A\in G$? If the whole proof of Niels Diepeveen correct?
Jan
2
revised Help to understand a proof (about filters)
$F$ is the cofinite filter, not an arbitrary free filter, I copied it wrong
Jan
2
asked Help to understand a proof (about filters)
Dec
28
accepted Both atoms and co-atoms in a lattice
Dec
18
awarded  Benefactor
Dec
18
comment Is a set closed under finite intersections? (about filters)
@KarlKronenfeld: You missed $y=0$ in the definition of $f_1$
Dec
18
comment Is a set closed under finite intersections? (about filters)
@KarlKronenfeld: $0\in f_1(1/n)$ for every $n\in\mathbb{N}$ because $(1/n,0)\in f_1$
Dec
18
comment Is a set closed under finite intersections? (about filters)
@KarlKronenfeld: Due funcoid magic $f_1\in\operatorname{GR} ( \Delta \times^{\mathsf{FCD}} \Delta) \Leftrightarrow f_2\in\operatorname{GR} ( \Delta \times^{\mathsf{FCD}} \Delta)$ and moreover $\operatorname{GR} ( \Delta \times^{\mathsf{FCD}} \Delta)$ is symmetric, see mathematics21.org/algebraic-general-topology.html
Dec
18
accepted Is a set closed under finite intersections? (about filters)
Dec
18
comment Is a set closed under finite intersections? (about filters)
@AlexRavsky: No! Your first comment was wrong. You provided a correct counter-example in your second comment. Please make an answer based on your second comment, not first!
Dec
18
comment Is a set closed under finite intersections? (about filters)
@AlexRavsky: I earlier wrote that your answer is not correct. That my comment was wrong and I deleted it. Really, your counter-example is correct. I suggest you to write it as an answer, so that I could accept it
Dec
17
comment Is a set closed under finite intersections? (about filters)
@AlexRavsky: It is not proved that there exists positive $\epsilon_1$ such that $f[\{x_1\}]\in\Delta$ for each $x_1\in(-\epsilon_1,\epsilon_1)$.
Dec
17
awarded  Yearling
Dec
12
comment Is a set closed under finite intersections? (about filters)
@KarlKronenfeld: Do you assume that $f$ is a function? $f$ is a binary relation, not necessarily a function
Dec
12
comment Is a set closed under finite intersections? (about filters)
@KarlKronenfeld: I added more parentheses to the formula. It seems you misunderstood me
Dec
12
revised Is a set closed under finite intersections? (about filters)
added more parentheses
Dec
12
awarded  Promoter