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A note on g -metrizable spaces

Jinjin Li — 2003

Czechoslovak Mathematical Journal

In this paper, the relationships between metric spaces and g -metrizable spaces are established in terms of certain quotient mappings, which is an answer to Alexandroff’s problems.

On k -spaces and k R -spaces

Jinjin Li — 2005

Czechoslovak Mathematical Journal

In this note we study the relation between k R -spaces and k -spaces and prove that a k R -space with a σ -hereditarily closure-preserving k -network consisting of compact subsets is a k -space, and that a k R -space with a point-countable k -network consisting of compact subsets need not be a k -space.

k -systems, k -networks and k -covers

Jinjin Li;  Shou Lin — 2006

Czechoslovak Mathematical Journal

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.

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