k-systems, k-networks and k-covers |
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| Authors: | Jinjin Li Shou Lin |
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| Institution: | (1) Department of Mathematics, Zhangzhou Teachers’ College, Zhangzhou, 363000, P.R. China;(2) Department of Mathematics, Fujian Normal University, Fuzhou, 350007, P.R. China;(3) Present address: Department of Mathematics, Ningde Teachers College, Ningde, 352100, P.R. China |
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| Abstract: | The concepts of k-systems, k-networks and k-covers were defined by A. Arhangel’skii in 1964, P. O’Meara in 1971 and R. McCoy, I. Ntantu in 1985, respectively. In this
paper the relationships among k-systems, k-networks and k-covers are further discussed and are established by mk-systems. As applications, some new characterizations of quotients or closed images of locally compact metric spaces are given
by means of mk-systems. |
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| Keywords: | k-systems k-networks k-covers k-spaces point-countable families hereditarily closure-preserving families |
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