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2
votes
2answers
145 views

Is certain topology-related set a distributive lattice?

In my research the following problem appeared (and if it is true, this solves positively several my conjectures): Let $U$ be a fixed set (usually $U$ is infinite). Let $n$ be a fixed index set ($n$ ...
0
votes
0answers
73 views

Carlson's translatability

I asked the following on MSE a few weeks ago but I did not get any answer : http://math.stackexchange.com/questions/1039593/carlsons-translatability-are-theses-characterisations-equivalent Given a ...
0
votes
1answer
109 views

Lowering from filters to ultrafilters for an infinitary relation

Let $U$ be a set. Let $N$ be a (possibly infinite) index set. Let $f$ be an $N$-ary relation on $U$ (that is $f$ is a set of functions $N\rightarrow U$). I denote $\mathcal{L}\in \upuparrows f ...
-1
votes
1answer
120 views

Expressing a value related to an infinitary relation through ultrafilters

Let $U$ be a set. I denote $\mathfrak{A}$ the lattice of filters on $U$ ordered reverse to set theoretic inclusion of filters. I denote $\bigvee$ and $\bigwedge$ correspondingly the supremum and ...
2
votes
1answer
100 views

Interweaving two indexed families of filters

Conjecture Let $U$ be an (infinite) set. Let $f$ be an $N$-ary (where $N$ is an arbitrary index set) relation on $U$ (that is a set of functions $N \rightarrow U$). Let $\mathcal{L}_0$, ...
4
votes
0answers
164 views

Intersections of open sets and $\alpha$-favorable spaces

I would like to ask about some classes of topological spaces whether they have been studied, what are they called (if they have a name) and whether they have some interesting properties. For the ...
2
votes
0answers
24 views

Analogous filter to Kalman filter that maximized mode instead (as opposed to minimizing variance)

I may have a potential application where maximizing the mode (as opposed to typically minimizing the variance) would be useful for state estimates. The situation may arise from skewed distributions ...
7
votes
1answer
348 views

A characterization of the poset of filters on a set

For the lattices of all subsets of a given set it is known an axiomatic characterization: A poset is isomorphic to a set of all subsets of some set iff it is a complete atomic boolean algebra. The ...
4
votes
1answer
215 views

Connection between subnet and superfilter

Let's define a net and subnet in this way: A net is any function of the form $n:(P,\le)\to X$ where $(P,\le)$ is a (preordered) directed set. A net $m:(P',\le)\to X$ is a subnet of the net ...
2
votes
0answers
266 views

Research in Algebraic Geometry involving Filters.

In Gillman and Jerrison's book, "Rings of Continuous Functions", they show a nice relationship between the set of z-ideals in C(X) and the set of filters on X. One can go for with this relationship; ...
3
votes
0answers
126 views

Theory of (definable) ideals on a multi-dimensional countable set

I'm wondering if there are any results about definable ideals/filters on $\omega\times\omega$, $\omega\times\omega\times\omega$, etc. To give a sense of the kind of results I might be looking for: ...
0
votes
2answers
300 views

Algorithm for calculating the sum-of-squares distance of a rolling window from a given line function

Given a line function $y = ax + b$, it is easy to calculate the sum-of-squares distance between the line and a window of samples $(1, y_1), (2, y_2), ..., (n, y_n)$ (where $y_1$ is the oldest sample ...
1
vote
1answer
136 views

Digital Filters [closed]

Can somebody help with the constructing filter by amplitude and phase spectrum? Is it possible? I try to google it, but unsuccessufully. I have some thoughts about solving it by system of linear ...
-11
votes
1answer
845 views

Direct product of filters

Product $a\times b$ of filters $a$ and $b$ is defined as the filter (on the set of binary relations) defined by the base $\{ A\times B | A\in a,B\in b \}$. I will denote the principal filter ...
-8
votes
2answers
1k views

Filters and intersection of two binary relations

Let $\mathfrak{F}$ is the complete lattice of filters (including the improper filter) on some set, ordered inverse to set-theoretic inclusion. I will denote $\left\langle f \right\rangle \mathcal{X} ...
0
votes
1answer
293 views

About ordering and equivalence of filters

Let $U$ is a set. I will speak about filters on this set. If $f$ is a function and $a$ is a filter then I define $f \left[ a \right]$ as the filter whose base is $\lbrace f[A] | A \in a \rbrace$. I ...
8
votes
6answers
750 views

Spaces of filters

This question arose more from curiosity than from an actual problem. There are situations when you embed some space $X$ in a set of filters on $X$, which inherits properties of $X$ or has even better ...
0
votes
1answer
339 views

Do filters complementive to a given filter form a complete lattice?

Really I should first ask this question here on MathOverflow and only then post it as an open problem in Open Problem Garden and propose it as a polymath problem. Indeed I did the reverse and now hope ...