关于更强形式的扩张性
On Stronger Forms of Expansivity
AI总结：
本研究提出正扩张映射的更强形式$p \mathscr{F}-$扩张映射的概念，构造相关实例、推导成立条件与性质，并研究半群下的$\mathscr{F}-$扩张同胚及逆极限空间移位映射的关联。
摘要：
我们定义了正扩张映射的更强形式这一概念，并将其命名为$p \mathscr{F}-$扩张映射，其中$\mathscr{F}$是自然数集$\mathbb{N}$的一个子集族。本文构造了正厚集扩张映射和正 syndetic 扩张映射的实例。同时，我们得到了正扩张映射成为正余有限扩张映射、正 syndetic 扩张映射的条件。此外，我们研究了$p \mathscr{F}-$扩张映射的若干性质，得到了用$p \mathscr{F}^*-$生成元刻画$p \mathscr{F}-$扩张映射的结论，其中$p \mathscr{F}^*$是$\mathscr{F}$的对偶族。我们将$(\mathbb{Z},+)$视为半群，研究了$\mathscr{F}-$扩张同胚，其中$\mathscr{F}$是$\mathbb{Z} \setminus \{0\}$的一个子集族。我们证明了紧度量空间上不存在满足$\mathscr{F}_s-$扩张性的扩张同胚。我们还研究了映射$f$的$\mathscr{F}-$扩张性与逆极限空间上移位映射$σ_f$之间的关系。
英文摘要：
We define the concept of stronger forms of positively expansive map and name it as $p \:\mathscr{F}-$expansive maps. Here $\mathscr{F}$ is a family of subsets of $\mathbb{N}$. Examples of positively thick expansive and positively syndetic expansive maps are constructed here. Also, we obtain conditions under which a positively expansive map is positively co--finite expansive and positively syndetic expansive maps. Further, we study several properties of $p \:\mathscr{F}-$expansive maps. A characterization of $p \:\mathscr{F}-$expansive maps in terms of $p \:\mathscr{F}^*-$generator is obtained. Here $p \:\mathscr{F}^*$ is dual of $\mathscr{F}$. Considering $(\mathbb{Z},+)$ as a semigroup, we study $\mathscr{F}-$expansive homeomorphism, where $\mathscr{F}$ is a family of subsets of $\mathbb{Z} \setminus \{0\}$. We show that there does not exists an expansive homeomorphism on a compact metric space which is $\mathscr{F}_s-$expansive. Also, we study relation between $\mathscr{F}-$expansivity of $f$ and the shift map $σ_f$ on the inverse limit space.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
