基数函数、Bornologies和强Whitney收敛
Cardinal Functions, Bornologies and Strong Whitney convergence
摘要：
设$C(X)$是度量空间$(X,d)$上所有实值连续函数的集合。Caserta在[A. Caserta，Strong Whitney convergence，Filomat，2012]，它是Beer-Levi在[Beer-Levi，Strong uniform continuity，J. Math. Anal.应用程序、2009年]。本文研究具有强Whitney拓扑和Whitney收敛拓扑的函数空间$C(X)$的各种基数不变量。在这个过程中，我们提出了一些结果从文献中简单的证明。最后，研究了$C(X)$上强Whitney收敛和强一致收敛性的基数不变量之间的关系.
英文摘要：
Let $C(X)$ be the set of all real valued continuous functions on a metric space $(X,d)$. Caserta introduced the topology of strong Whitney convergence on bornology for $C(X)$ in [A. Caserta, Strong Whitney convergence, Filomat, 2012], which is a generalization of the topology of strong uniform convergence on bornology introduced by Beer-Levi in [Beer-Levi, Strong uniform continuity, J. Math. Anal. Appl., 2009]. The purpose of this paper is to study various cardinal invariants of the function space $C(X)$ endowed with the topologies of strong Whitney and Whitney convergence on bornology. In the process, we present simpler proofs of a number of results from the literature. In the end, relationships between cardinal invariants of strong Whitney convergence and strong uniform convergence on $C(X)$ have also been studied.
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。
