关于R-半拓扑空间中连续性的一些结果
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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。
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.
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.
引文
[1]朱培勇,雷银彬.拓扑学导论[M].北京:科学出版社,2009.
[2]CSASZAR A.Generalized topology,generalized continuity[J].Acta Math,2002,96(4):351-357.
[3]MIN W K.Weak continuity on generalized topological space[J].Acta Math,2009,124:73-81.
[4]李阳,朱培勇.关于广义拓扑空间中的几乎连续性的一些结果[J].西南师范大学学报:自然科学版,2016,41(2):36-40.
[5]钟健,陈道富,朱培勇.关于R-半拓扑空间的一些结果[J].理论数学,2016,6:217-222.
[6]MIN W K.Almost continuity on generalized topological space[J].Acta Math,2009,125:121-125.
[7]CSASZAR A.On generalized neighbourhood systems[J].Acta.Math,2008,121(4):395-400.
[8]CSASZAR A.Generalized neighbourhood[J].Acta Math,2008,124(4):395-400.
[9]MIN W K.Some results on generalized topological spaces and generalized system[J].Acta Math,2005,108:171-181.
[10]SARMA R D.On extremely disconnected generalized topologies[J].Acta Math,2012,134(4):583-588.
[11]CSASZAR A.Generalized open sets in generalized topologies[J].Acta Math,2005,105:53-66.
[12]CSASZAR A.γ-connected sets[J].Acta Math,2003,101:273-279.
[13]CSASZAR A.Separation axioms for generalized topologies[J].Acta Math,2004,104:63-69.
[14]CSASZAR A.Products of generalized topologies[J].Acta Math,2009,123:127-132.
[15]Min WK.Generalized continuous functions defined by generalized open sets on generalized topological spaces[J].Acta Math,2010,128:299-306.
[16]李瑞佳,朱培勇.拓扑动力系统中强传递集的一些性质[J].四川理工学院学报:自然科学版,2016,29(6):90-93.
[2]CSASZAR A.Generalized topology,generalized continuity[J].Acta Math,2002,96(4):351-357.
[3]MIN W K.Weak continuity on generalized topological space[J].Acta Math,2009,124:73-81.
[4]李阳,朱培勇.关于广义拓扑空间中的几乎连续性的一些结果[J].西南师范大学学报:自然科学版,2016,41(2):36-40.
[5]钟健,陈道富,朱培勇.关于R-半拓扑空间的一些结果[J].理论数学,2016,6:217-222.
[6]MIN W K.Almost continuity on generalized topological space[J].Acta Math,2009,125:121-125.
[7]CSASZAR A.On generalized neighbourhood systems[J].Acta.Math,2008,121(4):395-400.
[8]CSASZAR A.Generalized neighbourhood[J].Acta Math,2008,124(4):395-400.
[9]MIN W K.Some results on generalized topological spaces and generalized system[J].Acta Math,2005,108:171-181.
[10]SARMA R D.On extremely disconnected generalized topologies[J].Acta Math,2012,134(4):583-588.
[11]CSASZAR A.Generalized open sets in generalized topologies[J].Acta Math,2005,105:53-66.
[12]CSASZAR A.γ-connected sets[J].Acta Math,2003,101:273-279.
[13]CSASZAR A.Separation axioms for generalized topologies[J].Acta Math,2004,104:63-69.
[14]CSASZAR A.Products of generalized topologies[J].Acta Math,2009,123:127-132.
[15]Min WK.Generalized continuous functions defined by generalized open sets on generalized topological spaces[J].Acta Math,2010,128:299-306.
[16]李瑞佳,朱培勇.拓扑动力系统中强传递集的一些性质[J].四川理工学院学报:自然科学版,2016,29(6):90-93.