-Ponomarev’s System and Images of Locally Separable Metric Spaces
Tran Van An, Luong Quoc Tuyen (2013)
Publications de l'Institut Mathématique
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Tran Van An, Luong Quoc Tuyen (2013)
Publications de l'Institut Mathématique
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Luo, Zhiming (2005)
International Journal of Mathematics and Mathematical Sciences
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Alexander Shibakov (1995)
Commentationes Mathematicae Universitatis Carolinae
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We prove some closed mapping theorems on -spaces with point-countable -networks. One of them generalizes Lašnev’s theorem. We also construct an example of a Hausdorff space with a countable base that admits a closed map onto metric space which is not compact-covering. Another our result says that a -space with a point-countable -network admitting a closed surjection which is not compact-covering contains a closed copy of .
Jinjin Li, Shou Lin (2006)
Czechoslovak Mathematical Journal
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The concepts of -systems, -networks and -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 -systems, -networks and -covers are further discussed and are established by -systems. As applications, some new characterizations of quotients or closed images of locally compact metric spaces are given by means of -systems.
Luong Quoc Tuyen (2013)
Publications de l'Institut Mathématique
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Shou Lin, Peng Fei Yan (2003)
Commentationes Mathematicae Universitatis Carolinae
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The main purpose of this paper is to establish general conditions under which -spaces are compact-covering images of metric spaces by using the concept of -covers. We generalize a series of results on compact-covering open images and sequence-covering quotient images of metric spaces, and correct some mapping characterizations of -metrizable spaces by compact-covering -maps and -maps.