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An amateur general topology researcher.


Sep
14
comment A conjecture about filters and finite unions of cartesian products
I provided a counter-example as an answer. That counter-example was wrong.
Sep
14
accepted A “rearrangement” of a finite set
Sep
14
awarded  Necromancer
Sep
11
answered A “rearrangement” of a finite set
Sep
11
comment A “rearrangement” of a finite set
For pairwise non-equivalent elements $a_0, \ldots, a_k$ we have $\forall i, j \in \{ 0, \ldots, k \} : (i \neq j \Rightarrow a_i \not\in X_{i, j} \wedge a_j \in X_{i, j})$ where $X_{i, j} \in T$. How to derive that $k \leqslant 2^n$?
Sep
11
comment A “rearrangement” of a finite set
@ThomasAndrews: I've spent more then a hour trying to prove this. I feel I am very near to the solution, but something prevents me to find it. Please explain how to derive the solution. It is not a homework and your help won't harm
Sep
11
comment A “rearrangement” of a finite set
@ThomasAndrews I feel that I am near to the answer. Probably I need to select a canonical representative element from every equivalence class
Sep
11
comment A “rearrangement” of a finite set
@ThomasAndrews I am stalled in the attempt to figure out the property of equivalence relations which corresponds to finiteness. Why would you not give me an answer? It is not a homework
Sep
11
comment A “rearrangement” of a finite set
@ThomasAndrews Maybe this is an eclipse in my mind. Why $S$ has at most $2^n$ elements?
Sep
11
comment A “rearrangement” of a finite set
@Hippalectryon I tried to meditate a half of minute and had no ideas
Sep
11
asked A “rearrangement” of a finite set
Sep
11
asked Terms for particular equivalence relation and partition?
Sep
11
revised A conjecture about filters and finite unions of cartesian products
joins -> unions
Sep
10
comment A lattice generated by two particular sublattices of the lattice of binary relations
@JairTaylor: Yes. Maybe the answer is the set of all finite unions of cartesian products?
Sep
10
comment A lattice generated by two particular sublattices of the lattice of binary relations
Maybe, it is the lattice consisting of all finite unions of pairwise non-intersecting cartesian products?
Sep
10
revised A lattice generated by two particular sublattices of the lattice of binary relations
added 55 characters in body
Sep
10
comment A lattice generated by two particular sublattices of the lattice of binary relations
@Keinstein: No, I mean all finite partitions of $U$ and every function $Y$ for a given partition. $Y$ is a mapping from $S$ into $\mathscr{P}U$ not from $\mathscr{P}U$ to $\mathscr{P}U$
Sep
9
asked A lattice generated by two particular sublattices of the lattice of binary relations
Sep
9
revised Another conjecture about filters and cartesian products
typo
Sep
9
revised Another conjecture about filters and cartesian products
minor correction