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Keywords:
$k$-systems; $k$-networks; $k$-covers; $k$-spaces; point-countable families; hereditarily closure-preserving families
$k$-systems; $k$-networks; $k$-covers; $k$-spaces; point-countable families; hereditarily closure-preserving families
Summary:
The concepts of $k$-systems, $k$-networks and $k$-covers were defined by A. Arhangel’skiǐ 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.
References:
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