On $k$-spaces and $k_R$-spaces

Jinjin Li

Displaying similar documents to “On $k$ -spaces and $k_{R}$ -spaces”

A note on transitively $D$ -spaces

Liang-Xue Peng (2011)

Czechoslovak Mathematical Journal

Similarity:

In this note, we show that if for any transitive neighborhood assignment $φ$ for $X$ there is a point-countable refinement $ℱ$ such that for any non-closed subset $A$ of $X$ there is some $V \in ℱ$ such that $| V \cap A | \geq ω$ , then $X$ is transitively $D$ . As a corollary, if $X$ is a sequential space and has a point-countable $w c s^{*}$ -network then $X$ is transitively $D$ , and hence if $X$ is a Hausdorff $k$ -space and has a point-countable $k$ -network, then $X$ is transitively $D$ . We prove that if $X$ is a countably compact sequential space and...

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

Jinjin Li, Shou Lin (2006)

Czechoslovak Mathematical Journal

Similarity:

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.

In search for Lindelöf $C_{p}$ ’s

Raushan Z. Buzyakova (2004)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

It is shown that if $X$ is a first-countable countably compact subspace of ordinals then $C_{p} (X)$ is Lindelöf. This result is used to construct an example of a countably compact space $X$ such that the extent of $C_{p} (X)$ is less than the Lindelöf number of $C_{p} (X)$ . This example answers negatively Reznichenko’s question whether Baturov’s theorem holds for countably compact spaces.

Displaying similar documents to “On k -spaces and k R -spaces”

A note on transitively D -spaces

k -systems, k -networks and k -covers

In search for Lindelöf C p ’s

Displaying similar documents to “On $k$ -spaces and $k_{R}$ -spaces”

A note on transitively $D$ -spaces

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

In search for Lindelöf $C_{p}$ ’s