# Questions tagged [filters]

The filters tag has no usage guidance.

8
questions

**4**

votes

**1**answer

177 views

### The property of the dense subfilter of a selective ultrafilter

Let us define the density of subset $A\subset\omega$ :
$$\rho(A)=\lim_{n\to\infty}\frac{|A\cap n|}{n}$$
if the limit exists. Let $\mathcal{F_1}=\{A\subset\omega~|~\rho(A)=1\}$. $\mathcal{F_1}$ is the ...

**4**

votes

**1**answer

105 views

### The example of the idempotent filter or subsets family with finite intersections property

From the answer of Andreas Blass and comments of Ali Enayat on my question Selective ultrafilter and bijective mapping it became clear that for any free ultrafilter $\mathcal{U}$ we have $\mathcal{U}\...

**-1**

votes

**1**answer

235 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 \...

**-2**

votes

**1**answer

293 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 ...

**8**

votes

**0**answers

718 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 ...

**4**

votes

**1**answer

170 views

### Convergent filters generated by (not necessarily countable) chains

Suppose $\langle X,\mathscr{O}\rangle$ is a topological space and let $\mathscr{O}_x$ be the family of all open neighbourhoods of $x\in X$. Let $\mathscr{F}$ be the filter generated from $\mathscr{O}...

**5**

votes

**1**answer

398 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 $n:(P,\le)\...

**2**

votes

**1**answer

168 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 $\mathcal{L}_0$, $\...