All Questions

Let $\{a_n\},\{b_n\}$ be strictly increasing sequence of positive integers satisfying $a_1<b_1<a_2<b_2<a_3<b_3<\ldots$ and $(b_n-a_n) \to \infty$. Define $I_n:= [a_n,b_n]$, meaning ...

Let {$q_i$} be a list of all rationals, $U_{i,n}$ be an open interval centered at $q_i$ with length of $2^{-i}/n$. Then open set $\bigcup_{i}U_{i,n} $ has the length of $1/n$ and contains all ...

Let $f:\omega\to\mathbb N$ be a function such that $\sum_{n=0}^\infty\frac{f(n)}{2^n}<\infty$. We identify each natural number $n\in\mathbb N$ with the set $\{0,\dots,n-1\}$. Then the map $$\...

Let the height of a poset $P$ be the supremum of ordinals that are order types of all well-ordered subsets of $P$ (with order inherited from $P$). Define several sets of total functions, in each ...