强邻近连续\& Strong Connectedness
Strongly Proximal Continuity \& Strong Connectedness
摘要：
本文引入强邻近连续（s.p.c.）函数，强邻近等价（s.p.e.）和强大的连通性。主要结果是：若拓扑空间$X,Y$具有相容强逼近且$f:X\longrightarrow Y$是双射s.p.e.，则它在超空间$\CL(X)$和$\CL(Y)$上的扩张是一个同胚，并赋予了相应的强击中和击不中超拓扑.对于一个被赋予强近邻近的拓扑空间，强近邻近连通蕴涵着连通性，但反之则不然。给出了强邻近连通性所需的条件。s.p.c.的应用和强邻近连通性是根据强邻近描述性邻近给出的。
英文摘要：
This article introduces strongly proximal continuous (s.p.c.) functions, strong proximal equivalence (s.p.e.) and strong connectedness. A main result is that if topological spaces $X,Y$ are endowed with compatible strong proximities and $f:X\longrightarrow Y$ is a bijective s.p.e., then its extension on the hyperspaces $\CL(X)$ and $\CL(Y)$, endowed with the related strongly hit and miss hypertopologies, is a homeomorphism. For a topological space endowed with a strongly near proximity, strongly proximal connectedness implies connectedness but not conversely. Conditions required for strongly proximal connectedness are given. Applications of s.p.c. and strongly proximal connectedness are given in terms of strongly proximal descriptive proximity.
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。
