arXiv subjects
Publications and source records attributed to Josef Eschgfäller.
For every finite closure space $X$ one can define a finite topological space $\operatorname{Top} X$ together with a natural projection $\operatorname{Top} X\longrightarrow X$. This could allow to apply the techniques of topological combinatorics to the study of finite closure spaces.
Let $f:T\longrightarrow T$ be a mapping and $Ω$ be a subset of $T$ which intersects every (positive) orbit of $f$. Assume that there are given a second dynamical system $λ:Y\longrightarrow Y$ and a mapping $α:Ω\longrightarrow Y$. For $t\in T$ let $δ(t)$ be the smallest $k$ such that $f^k(t)\inΩ$ and let $t_Ω:=f^{δ(t)}(t)$ be the first element in the orbit of $t$ which belongs to $Ω$. Then we define a mapping $F:T\longrightarrow Y$ by $F(t):=λ^{δ(t)}(t_Ω)$.
We introduce several classes of pseudorandom sequences which represent a natural extension of classical methods in random number generation. The sequences are obtained from constructions on labeled binary trees, generalizing the well-known Stern-Brocot tree.