Some weak versions of the $M_{1}$-spaces

Fucai Lin; Shou Lin

Some weak versions of the $M_{1}$-spaces

General Topology 2013-02-19 v1

Authors: Fucai Lin , Shou Lin

Abstract

We mainly introduce some weak versions of the $M_{1}$ -spaces, and study some properties about these spaces. The mainly results are that: (1) If $X$ is a compact scattered space and $i(X)\leq 3$ , then $X$ is an $s$ - $m_{1}$ -space; (2) If $X$ is a strongly monotonically normal space, then $X$ is an $s$ - $m_{2}$ -space; (3) If $X$ is a $\sigma$ - $m_{3}$ space, then $t(X)\leq c(X)$ , which extends a result of P.M. Gartside in \cite{CP}. Moreover, some questions are posed in the paper.

Keywords

$M_{1}$-spaces compact scattered spaces strongly monotonically normal spaces $\sigma$-$m_{3}$ spaces tightness cellularity

Cite

@article{arxiv.1302.4200,
  title  = {Some weak versions of the $M_{1}$-spaces},
  author = {Fucai Lin and Shou Lin},
  journal= {arXiv preprint arXiv:1302.4200},
  year   = {2013}
}

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8 pages

Some weak versions of the $M_{1}$-spaces

Abstract

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