Displaying similar documents to “The class of ℵ -spaces is invariant of closed mappings with Lindelöf fibres”

Closed mapping theorems on k -spaces with point-countable k -networks

Alexander Shibakov (1995)

Commentationes Mathematicae Universitatis Carolinae

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We prove some closed mapping theorems on k -spaces with point-countable k -networks. One of them generalizes Lašnev’s theorem. We also construct an example of a Hausdorff space U r with a countable base that admits a closed map onto metric space which is not compact-covering. Another our result says that a k -space X with a point-countable k -network admitting a closed surjection which is not compact-covering contains a closed copy of U r .

k -systems, k -networks and k -covers

Jinjin Li, Shou Lin (2006)

Czechoslovak Mathematical Journal

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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 m k -systems. As applications, some new characterizations of quotients or closed images of locally compact metric spaces are given by means of m k -systems.