Bulletin

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Volume 36 • Number 4 • 2013

• Metrizability of Rectifiable Spaces
Fucai Lin

Abstract.
A topological space

$G$ is said to be a {\it rectifiable space} provided that there are a surjective homeomorphism

$\varphi :G\times G\rightarrow G\times G$ and an element

$e\in G$ such that

$\pi_{1}\circ \varphi =\pi_{1}$ and for every

$x\in G$ we have

$\varphi (x, x)=(x, e)$ , where

$\pi_{1}: G\times G\rightarrow G$ is the projection to the first coordinate. In this paper, we firstly show that every submaximal rectifiable space

$G$ either has a regular

$G_{\delta}$ -diagonal, or is a

$P$ -space. Then, we mainly discuss rectifiable spaces are determined by a point-countable cover, and show that if

$G$ is an

$\alpha_{4}$ -rectifiable space determined by a point-countable cover

$\mathscr{G}$ consisting of bisequential subspaces then it is metrizable, which generalizes a result of Lin and Shen's.

2010 Mathematics Subject Classification:54A25, 54B05, 54E20, 54E35

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