Let's define a net and subnet in this way: A net is a 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 subne …

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 …

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 migh …

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 $X$ …

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 $y_1$ i …

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 s …

Below is a special case of a general research problem I try to attack. Let $\mathfrak{A}$ be a poset. Free stars on $\mathfrak{A}$ are such $S\in\mathscr{P} \mathfrak{A}$ that the …

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 …

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 …