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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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Currently displaying 1 – 3 of 3

A note on g -metrizable spaces

On k -spaces and k R -spaces

k -systems, k -networks and k -covers

A note on $g$ -metrizable spaces

On $k$ -spaces and $k_{R}$ -spaces

$k$ -systems, $k$ -networks and $k$ -covers