Reputation
Top tag
Next privilege 2,000 Rep.
Edit questions and answers
Badges
6 19
Newest
 Custodian
Impact
~67k people reached

1d
comment Duals of filters, an explicit formula for meet?
After some thinking, I conclude that it seems that there is no explicit formula in this case
2d
comment Duals of filters, an explicit formula for meet?
@AsafKaragila You've misunderstood. Ideal is a filter in dual order. But I take both dual order (that is replacing every element of the filter with its dual) and complement of the filter (considered as a set)
Jun
16
comment Characterization of monovalued functions
For every $x$ there are no more than one $y$ such that $(x,y)\in f$
Jun
16
comment Characterization of monovalued functions
$f=\varnothing$ is a function. I define function as a monovalued (including zero-valued) binary relation
Jun
16
comment Characterization of monovalued functions
I did a stupid thing: I got a 100 points bounty for this easy question. I've solved it myself soon after this. For a solution consider $G=\{\{(a;y)\};\{(b;y)\}\}$ for $a\ne b$
Jun
14
comment Labeled commutative diagram
Another question is how to paint such a diagram. For every node we need both an object and a label. Two symbols can't be in one place
Jun
14
comment Category theory: Enough that polygonal diagrams commute
@Unit "pentagonal" was a typo. Corrected
Jun
14
comment Prove that all cycles are identities
I want a more detailed proof
Jun
13
comment An alternate definition of ideals
It seems that we need an additional condition: $P$ contains dual poset of each element of $P$
Jun
13
comment An alternate definition of ideals
a key to this proof is decomposition $\theta = \operatorname{dual} \circ \omega$ where $\omega$ is an order isomorphism on $P$. It remains to fill proof details. It is easy to show that $\omega[\mathfrak{F}] = \mathfrak{F}$, but we need stronger formula $\omega[\mathfrak{F}\cap P] = \mathfrak{F}\cap P$
Jun
2
comment Categories of $n$-ary relations?
Relations (not only binary relations) form a "category with star morphisms" (over $\mathbf{Rel}$) as I define them in my book: mathematics21.org/algebraic-general-topology.html - I suspect that I am the first person who explicitly defined categories with star morphisms, as they are important for my research of products of morphisms.
May
23
comment About elements of a poset
Counterexample: mathematics21.org/binaries/star-comparison.pdf (suggested by sci.math people)
May
8
comment The least relation which produces a partial order
(stupid comment removed)
May
7
comment The least relation which produces a partial order
@PedroM. $E^2 = E\circ E$ is the composition of binary relation $E$ with itself
May
2
comment What do the symbols d/dx and dy/dx mean?
It is described in en.wikipedia.org/wiki/Differential_of_a_function
May
1
comment What do the symbols d/dx and dy/dx mean?
@Fixee See my answer. It is nevertheless CAN be defined as a fraction of two functions, rather than an atomic object.
May
1
comment What do the symbols d/dx and dy/dx mean?
Note that $\frac{F}{G}$ is defined for two functions $F$ and $G$ as $\frac{F}{G}(x)=\frac{F(x)}{G(x)}$. Thus $\frac{df}{dx}$ makes sense.
Apr
29
comment Three theorems for the price of one? (like duality)
en.wikipedia.org/wiki/Triality (for vector spaces)
Apr
29
comment Three theorems for the price of one? (like duality)
@HagenvonEitzen Why six?
Mar
26
comment An elementary proof about filters
@AndreasBlass: You are right, the first $\bigcap$ on the right side of the equation was intended to be $\bigcup$. I've corrected the question.