【摘要】 借鉴一般拓扑空间与广义拓扑空间中连续性的定义方法,首先给出R-半拓扑空间中逆开连续、点态连续的定义,并得出逆开连续一定是点态连续,点态连续不一定是逆开连续的结论;又给出R-邻域系统的定义,并进一步给出在R-邻域系统上连续、弱连续、几乎连续、强连续的定义,研究了几种连续之间的关系。指出在R-邻域系统上的强连续严格强于连续,连续严格强于弱连续;强连续严格强于几乎连续,几乎连续严格强于弱连续;几乎连续与连续无关。更多还原

【Abstract】 The notion of opening the inverse continuity and pointwise continuity on R-semi-topology has first been pointed out,reaching the conclusion that opening the inverse continuity has been pointwise continuity and their relationship is not constant. Inaddition,the notion of R-neighborhood systems has been introduced. At the same time,the notion of continuity,weak continuity,almost continuity and strong continuity have been further introduced,then the relationship between them has also been investigated. It has pointed out that the strictness of strong continuity in the R-semi-topology is stronger than continuity; The strictness of continuity is stronger than weak contiuity; The strictness of almost contiuity is stronger than weak contuity. However,alomost continuity is independent of contonuity.更多还原